We are planning a trip to Sicily in May 2014 for about 9-10 days. First thought were to hire a car but then we thought maybe we could base ourselves in say Palermo for 5 nights and Taormina for 5 nights and do bus or train trips to see both areas. We live in Australia and Europe is a bit more difficult for driving.
Any suggestions would be greatly appreciated.

I would get a car. Not for Palermo but for the drive to the other side of the island. Stop in Agrigento for a night along the way. I think 5 nights (4 days) in Taormina would be way too long. It's good for an afternoon but not much more. I'm wondering if the bus connections would be better from Syracusa or Ortygia.

I loved Palermo - it was my favorite place that I saw on Sicily. You can take trips to the beach and to Cefalu (charming town with nice beach), and to Monreale.

If I can drive in England, Scotland, and Malta then you can drive on Sicily!

I didn't think driving in Sicily was bad (we picked up the car at the airport in Palermo, did not drive in the city itself). Wish we had hired the GPS though, as we got lost often just relying on maps.

I loved Sicily, including Palermo. We stayed in Palermo, Agrigento, Modica and Syracusa (on Ortygia).

It is definitely possible to visit Sicily without a car if that is your preference. There were a few trip reports about doing so on this board some years back, so you might want to see if you can find them. And some of us did find the drivers on Sicily a bit on the crazy side -- OMG!!! The roads were generally fine, but speeding cars that take even blind curves too fast while driving in between the marked lanes, which were full of speeding bumper-to-bumper traffic (literally) make me a tad nervous. One thing to keep in mind, though, is that using public transportation will probably mean that you won't be able to see as much of Sicily as you would be able to do if you had your own car, and 9-10 days is not much for Sicily. (Many of us think it deserves at least 2 weeks.) If you are open to considering a car for part of the trip, renting one to get from Palermo to Siracusa worked very well for me. As already suggested, you could stop in Agrigento (and maybe Segesta and/or Selinunte and/or the Villa Romana del Casale) en route.

Public transportation on the east side will almost certainly be easier from Siracusa than Taormina.

Driving in Sicily isn't as "scary" as driving in Naples - let's talk chaotic with a hefty mix of crazy! (And I still loved it!), and driving on the opposite side of the road to what you're used to doesn't take long to get the hang of, just going around roundabouts can be a little tricky (the first time you do it you'll know what I'm talking about). Having a car will allow you to explore so much more and to also go at your own pace without adhering to timetables of trains/busses.

Although there is definitely merit to basing yourselves in 2 places with day trips, it's also good to be able to spend a night or two in some other places. Siracusa is one place I would recommend staying in for a few nights - there's nothing better than being able to wander around after dinner without the worry of having to drive back to your accommodation in another town.

Click on my name above to find my tip report for May of 2005.
We had a car for most of the time.

OBIE31,

Bob's trip report of 2005 (and kja and thursdayd's) inspired my visit this year in April. Highly recommend you read all these report and get a good idea of how much there is to see and do in Sicily.

I absolutely loved it! I was a bit worried right before I because I had such high expectations and so many years of anticipation.....Sicily surpassed my expectations.

Driving was very easy. I had a car for 9 days, picking up and dropping in cities with no problems at all. I used a Tom Tom GPS and paper maps as backup.

With just 10 days, you will have to choose. Just one temple site, one nature preserve, one museum, etc. My own trip was almost a month and it wasn't long enough.

click on my name and those of the other posters mentioned above to see their trip reports.