My favorite part of Prague is the Jewish neighborhood, particularly the cemetery. For restaurants I go outside of the old town... Below is a Prague trip report with our favorite restaurants. Enjoy!

http://worldinbetween.wordpress.com/2012/07/16/3-days-in-prague-on-and-off-the-beaten-path/

http://www.prague.net/itineraries-in-prague
this link will give you lots of info on what to see and do.
and this one lots of other info and some discount vouchers and meal deals.
http://www.livingprague.com/
this link is a great resturants Blog and worth a read.
http://czechoutchannel.blogspot.co.uk/
Prague has such a wide range of things do do and see but my favoyrites include the Strahov monastry, The whole of the castle area but sepecuaially the armoury area in Golden lane, Charles bridge ( I can walk up and down there all day,)and the Municiple House.
In June the weather should be nice and my No1 recommendation is to visit letna park (http://travel.yahoo.com/p-travelguide-2773249-letna_park_prague-i)
, the views from here are quite stunning and this is where pics of the Prague bridges are taken,The Havansky Pavillion id the best spot and it is a fine but expensive place for a drink or a meal.
Along a bit is a huge beer garden and is a spot I always head for in the good weather.

bookmarking

BMK

Those bookmarking , have a look at many of my previous threads ,lots of good info there.I have been visiting the czech republic and Prague for over 20 years now and am there at least once a year and often 2 or three times, i sometimes lead small walking groups in the area.My next visit is in May for the Czech Beer festival an annual must see event for me.
http://www.ceskypivnifestival.cz/en/

unclegus, I have been reviewing your fabulous threads as well. I'm in the very early planning stages and looking at mid-September. Trying to find that fine balance between the time the summer travelers are gone but before it gets too cold.

september is a great time ,I was in prague in late october last year and it was suprisingly warm ,so much so one night I actually went back to my apartment and left my jacket.
Prague is always busy with tourists year round but once July and August are over things are slightly lest manic.
I suggested in my first post about visiting Letna park and that holds at anytime of the year,the beer gardens stay open until it gets too cold to sit outside and I did have a beer there in the afternoon in october sitting with a view over the river it was quite lovely, the Havansky pavillion is open all the year round.

I am back in Prague from the 23rd-30th May (Beer Festival time) I won't be in the city center much but if any of you want me to check anything out i can make a few detours and get back to you when I am home.

Regardless of what anybody says, I think you should at least take a stroll if nothing else, in the area surround the astonomical clock.

Yes, the place is often crowded with visitors. Yes, those outdoor restaurants don't necessarily serve the greatest food. Yes, those people who cut out your silhouette with scissors from afar and then try to sell you the results are for some people a pain. But this is as much a part of Prague as anything else and I think it is worth your time.

I can't disagree with what Dukey says, there are some nice spots around the Old Town square and yes you do pay well over the odds for so so food and drinks but hey you are on your holidays and Prague is still relatively cheap compared to other european cities. The Hotel U Prince is the ideal spot for the Astronomical clock and they have a roof terrace you can go up and observe the crowds down below.
Can't say I have ever experienced the silhouette folk but maybe i am too ugly for them.

One thing we enjoyed was walking across the St Charles bridge late at night. The towers were lit up and the street lamps were lit as well.

The towers turn off precisely at midnight...ask my husband who set up his tripod and camera and then went to take the picture just when the tower light went off. Arghhh. It was our last night there so no redos on that one. But still beautiful to remember.

We also enjoyed just roaming up and down the streets with no particular destination in mind. You find some fun stuff that way.

A lovely, peaceful spot in crowded Prague iare the beautiful gardens of the Wallenstien Palace (Czech Senate building). Bring a sandwich and have a picnic lunch!

I like what every everybody has said here.

But you can hardly go wrong in Prague ( unlike some other cities)

The greatest attraction if Prague is "The City Itself"

I know you are asking ,"What do you mean "?

Well in Prague you can just stroll around the Old Town, the new Town ,the Jewish Quarter ...and you will see what I mean !!!!

Because some neat attraction can be found around every corner, and some of the great pleasure is to just walk aimlessly around, and admire the beauty in the people, places and architecture.

Of course there are Special Attractions like:

Prague Castle
Charles Bridge
Old Town Square and
Astronomical Clock
Jewish Cemetery
Wallenstein Palace and Grounds.

This is not to say that you should not do your homework on Prague.... but if you came here "cold turkey". you would still love the place.

The Loreto Church! Gorgeous!

PDersch:
You can add to your list:
The "Dancing Houses"; and on the opposite margin of the river, the Memorial to the Victims of Communism.
No doubts Praga is an ejoyable and walkable city.