What are the "must-do's" in prague?

Charles bridge, castle hill, market square with the clock, ...

Check also this http://wikitravel.org/en/Prague

What time of year? I'd generally spend a lot of time in parks and beer gardens..

I like Petrin Hill too. You can take the funicular up (there's a decent restaurant halfway up too with good views), walk around and if you have the stomach for it, climb Petrin Tower. It's 300 steps and designed similar to the Eiffel Tower...amazing views from the top.

If you're interested in war stuff, the Czech Military Museum is quite good (and free!) and this is a really moving place to go:

http://en.wikipedia.org/wiki/Church_..._and_Methodius

The Prague Zoo is fantastic if you have extra time.

Jewish quarter/cemetery ?

Just having a wander around the streets away from the tick-it-off sites is also pleasant (although I do that everywhere, drives Mrs C mad).

Agree, Prague has a lot of interesting areas away from the main tourist attractions.

And there are always concerts etc. in Prague. See this site for information about what is on when :
http://www.pragueexperience.com/oper...a_concerts.asp

Ah yes, forgot that, we went to see a classical music/ballet concert at the Municipal House (IIRC), just down the road from the Hilton Old Town.

V good & inexpensive.

And I went for the Bolero concert in the Spanish Synagoge. Also very good.

In addition to the castle, which pretty much takes a whole day to see it all, I found the Jewish quarter quite interesting. Also there is a somewhat offbeat Museum of Communism that I found amusing and interesting; it's next to a casino and a McDonalds.

should have mentioned my travel date. I will be there last week of November

Maybe you are lucky enough for the christmas markets to have started. Check it out. Really nice markets and lots of fancy christmas lights all over.

And another must do in Prague - eat.
I can highly recommend this restaurant if you like meat :

http://cestr.ambi.cz/en/#index

I have Nov 26-Nov 30 to split up my time between Rome and Prague.
I was going to do Nov 26(arrive in Rome from Milan around 6pm) then leave Rome Nov 29 to Prague. Leave Prague on Dec 1 early morning.
Leaves me only 1.5 days in Prague.

Should I shorted Rome and get extra day in Prague? I've never been to both places.

If you've never been to either, Rome is more traditional tourist with ruins etc. Prague has a ton of history as well, but there's no Colosseum. I would probably keep your itinerary, you can always go back.

I spent a week in Prague last month and prefer it to Rome. But it's different and I'm glad I went to Rome and some other places years ago before Prague.

As other said, the castle is impressive and takes most of a day if you go through all of the grounds. But you could abbreviate it and just see the highlights. There's also Karlstejn Castle, but that's 40 minutes outside Prague so if you only have 1.5 days, probably not. And sort of random, but I thought the KGB museum was hilarious. It's not cheap for Prague, but the tour guide/owner/host/only employee is very entertaining.

The Prague christmas markets open on the 29. of November so perfect timing.
With so little time there, don't try to do too much. Give yourself time to just stroll around also.