In St. Kilda, try Cicciolina (they take reservations for lunch but not for dinner).

http://www.cicciolinastkilda.com.au

In town, try Maha, Red Spice Road, Spice Temple (sit downstairs).

http://www.mahabg.com.au/about-maha.htm
http://www.redspiceroad.com
http://www.spicetemplemelbourne.com

For Vietnamese, go to Victoria Street in Richmond.

For Italian, there's Lygon Street though many of them are of the 'tourist trap' variety; in town, try Il Solito Posto, Becco, Il Bacaro. For something different and more down to earth, The Waiters Club.

For breakfast/brunch/lunch/dinner, try The European on Spring Street.

Much of Melbourne (in the CBD) is hidden down an alleyway, up a grungy looking flight of stairs or down in a basement -- don't be put off.

For bars, try the Melbourne Supper Club (a more-or-less unmarked door on Spring Street, next to the European) or Siglo, further upstairs at the same address. Also try Cookie, The Toff In Town (both up the stairs at the unmarked 252 Swanston Street), Madame Brussels, Order of Melbourne, MOO (Money Order Office), Section 8, New Gold Mountain, Double Happiness, The Deanery, The Transit Lounge at Federation Square (top floor, above the Transport Hotel <nothing to recommend it> and Taxi Dining Room (which is good). Go and see Chloe, upstairs at the iconic Young and Jacksons, opposite Flinders Street Station. On the opposite corner, go and sit in St. Paul's Cathedral for 5 minutes of quiet reflection. Get on a tram down St. Kilda Road to the Belgian Beer Garden.

Melbourne is the coffee capital of Australia and it's pretty hard to get a bad coffee. There are a few Starbucks around but no self-respecting Melburnian would be caught dead in one.

If you like jazz, go to Bennetts Lane.

As for Phillip Island and the penguins, I've never understood the attraction (and have never been) - to each their own.

If you like wineries, a day out in the Yarra Valley is always nice, an easy hour or so drive from town. Start with a cheese tasting plate at the Yarra Valley Dairy Company, visit Domain Chandon (and try a tasting flight of their sparkling wines), then on to the art gallery at Tarra Warra, have lunch there or at De Bortoli or Yering Station or Tokar Estate.

These are great suggestions and I'm excited about the coffee. I'm from Venezuela (where coffee is out of this world) and I think that Starbucks is just a bit better than American coffee ( I live in the US)

What should we visit in Sydney?

In Sydney the harbor is fantastic - a cruise will give you views of the Opera House and from circular key ferries provide public transport to many northern suburbs. The Rocks is an historic area of Sydney and nearby Darling Harbor for shopping and the Museum of Contemopary Arts, Maritime Museum and the Aquarium on Cockle Bay provides plenty to see and do. The Powerhouse Museum and Chinatown is a short distance also but with limited time in Sydney the museums are probably too much to squeeze in.

The harbour cruise is a good idea but an easy way to do it is to take the ferry to Manly (takes about 30 minutes or so). On the way out to Manly, you pass across The Heads, the entrance to Sydney Harbour from the Pacific. When you get off the ferry in Manly, cross the street and walk up The Corso to the beach. Turn right and you'll find various cafes and restaurants - have breakfast/coffee/lunch/a beer, depending on the time of day. Take the ferry back.

Taronga Zoo is well worth a visit. You can get there by ferry (again from Circular Quay). You can get a combined ferry/zoo ticket.

If you like Thai food, try The Canteen (upstairs) at Sailors Thai - 106 George Street, in The Rocks.
http://www.sailorsthai.com.au

Visit the Opera Bar, alongside the Opera House. Sit and have a drink, watch the ferries, watch the micro-organisms (humans) climbing the Bridge, enjoy the view.

Climb (or walk) the Bridge. The climb is somewhat expensive but worthwhile - a great experience.
http://www.bridgeclimb.com

Go for a walk in the Botanic Gardens and visit Mrs. McQuarie's Chair.
http://en.wikipedia.org/wiki/Mrs_Macquarie's_Chair

Go out to Bondi to the beach. Go for a walk along the cliffs to Bronte etc.

There used to be a "Red" bus and a "Blue" bus, two hop-on, hop-off buses that followed different routes, both starting/ending at Circular Quay (so it was easy to do one and then the other). They were a great way to see the highlights of Sydney, even if you just stayed on the bus all the way round. Those are now gone, I think, and replaced by ..... I'm not sure what? Would have to do some homework or perhaps a Sydneysider can jump in and provide advice. The Blue Bus used to go to Bondi, though there are other buses that will get you there and back.

In Melbourne, try and fit in the Tramcar Restaurant (basically an old heritage tram converted to a restaurant). Great views of the city in a slow old-fashioned way to travel, plus great food. May require booking in advance as they are very popular.

http://www.tramrestaurant.com.au/

I always recommend the bondi to bronte ( or further to coogee) walk...easy and you will experience what beach culture is like for sydneysiders
have lunch or coffee at bronte and then decide whether you want to go further on to coogee which involves walking along streets rather than the beach cliff walkways

you can then catch the bus back from coogee to your city accommodation should you choose to do so

palm beach is also nice..harder to get to by public transport but worth it ..beautiful walk up to the lighthouse ( check the website to see what days the lighthouse is open) the views are really something!

You all are great!!!! I'll start putting a firm plan together

Just got back from our first trip to OZ, and for Sydney, I strongly recommend Taronga Zoo, esp. if you are interested in birds (and animals, of course) - it's a very special one. I also second the recommendation of the Bondi Beach to Bronte or Congee Beach walk. We did that last week. It took about 2 hours, with stops for photos and food. Bus 383 (I think) to Bondi starts at Circular Quay, and the Coogee bus (diff. number, ask your concierge) stop back is right at the beach. Restaurant in the Rocks area - Wine Odyssey Australia was lovely, but not cheap.

All suggestions sound great. I have a few more questions:

-any advice on seats at the Opera House. We want to buy tickets for Il Trovatore. Considering circle C
-do we need to reserve in advance for the opera house tour?
-do we need to reserve in advance for the at our cruise?

Being summer, is it best to do the bridge climb at dawn or evening?

It's best to book a bridge climb for dawn. If it's a really hot day you will be cooking in those cute little jumpsuits.

Re the Opera House. If you book Circle C you will be probably be way at the back (rows G -P) - at least that's usually the way it works. If you have opera glasses it will be ok - if you don't, you will probably be wishing you were a bit closer. The earlier you book the better your seats will be.

Yes, do book for the tour so you can get the one of your choice. It's our main school holiday during January and one of the busiest times at the Opera House.

Before you do anything in Sydney, go inside the building called the Customs House which is opposite Circular Quay. Just inside the door you will see a public library to the left. Don't go into the library - keep walking straight into the large foyer and you will come to a most marvellous model of Sydney with a heavy glass top which you walk over, (or crawl on all fours like me!). It gives you a great perspective of the city before you start exploring. http://www.cityofsydney.nsw.gov.au/customshouse/visiting/model.html

In Sydney, if you like walking take a stroll around the area close to the city called Paddington. It's a historical suburb with lots of interesting little galleries, shops and cafes in between the terraced houses.

I have two favourite places to eat in Sydney, and food has to be pretty good to get me inside a restaurant - first is Billy Kwong http://www.kyliekwong.org/BillyKwongs.aspx It's tiny with no-back chairs, but the food is delicious. You can either make a reservation or just turn up and hope for a seat.

The other is a high end (read=bit pricey) Vietnamese restaurant called Red Lantern. http://www.redlantern.com.au/crown/

If I can remember the name of my current favourite coffee place I'll post again. Have fun planning.

try to visit centrepoint tower in the city at the outset so that you get an orientation of sydney..especially the coastline
you can have dinner up there ..its ok...not fantastic but adequate
try to get up there just before dusk so that you see the city and then watch it come to life after dark...so so pretty and one of the nicest city views in the world, i think

In Sydney, it's free to walk across the Harbour Bridge. The Bridge climb is very expensive, I think it's a total tourist rip-off, that said friends from overseas who have done it really enjoyed it.

If you want a great view of Sydney go to the bar in the Summit top floor of Australia Square (designed by Harry Seidler) an iconic Australian modernist building that is worth seeing in its own right. The bar (and restaurant) rotate so you get to see the whole of Sydney, it opens at 5 pm so it's a great place to view sunset.

For four days, I would also recommend one of the beach walks (Bondi to Bronte). The bus from Circular Quay is the 380 or the 333. I'd also suggest visiting the Art Gallery of New South Wales for the collection of Aboriginal Art. The restaurant has a great view. Other museums that could be of interest: Museum of Sydney, Museum of Contemporary Art. The latter has a restaurant on the top floor with an amazing view of the harbour.

If you are interested in colonial/convict history, the Hyde Park Barracks is interesting museum. Cockatoo Island is another interesting convict site. There's also an outdoor bar there (the Island Bar) that's great on a sunny day.

My favourite restaurants in Sydney are: Momofoku (sublime, recently voted best restaurant in Sydney), Berta (Italian), Movida (Spanish, also in Melbourne), Spice Temple (Modern Asian now also in Melbourne), Porteño (Argentinian). I also like Billy Kwong and Red Lantern.

The Opera Bar at Circular Quay near the Opera House is fun for people and ferry watching. From here you can watch the tiny grey specs cross the Harbour Bridge in groups.

I believe climbing the Harbour Bridge is very popular so book early if you are limited in the number of days you have available.

Just came back and loved it. YOUR suggestions were excellent!!!! The weather was great and the sites were amazing.

Loved:
The opera House tour, Il Trovatore and the Opera Bar.
Manly Beach, Watson Bay (where the bay starts!) and Bondi
The Goverment House and the gardens (amazing trees)
The Australia open was great, the 12 Apostles and St Phillip Island.
Lunch at Rockpool (Melbourne), Jaimie Oliver and at St Phillip Island Isola di Capri were excellent
Most tours were excellent....some a bit too long.

If it was a bit closer and not so expensive I would go back....the 16 hour flight sucked the life out of me!!!

Great to get your feedback. When you have time perhaps you can tell what tours were too long or just right.

Do you know that you were here in the hottest January in Australia's history? Hope you found some cool spots.

The weather was FANTASTIC both in Melbourne and Sydney, I missed the bad weather I guess. The hottest was 85 and it felt hotter because we were at the Australia Open. One day in Sydney it rained but other than that highs were 70's and lows were 50's. I was glad to have brought a jacket because I used it ever day.
The tour to the Great Ocean Road was 12 hours (over 500 KM) and the bus we were given was not a comfortable one....so it seemed longer than 12 hours. That is one tour worth doing in 2 days if one has the time.
The tour to St Phillips Island was good (12 hours also). they picked us ip at noon and we were back at the hotel at midnight (Pinguins come out of the water past 9 pm)

One other thing to comment on was that we read great reviews for Messina's gelato on Trip Advisor....we walked a good distance to find it in Sydney and found it to be below average...Gelatisimo (which seems to be everywhere) was better.
I LOVED coffee in Australia.....it was good everywhere.....expensive yes, but great!