Personally, I would get something like the Lonely Planet Czech phrasebook or Assimil or Teach Yourself, learn some phrases of interest to you and use them. I found lots of people in Prague who would try to understand my Czech or give me corrections instead of switching to English. Outside the tourist center I found pubs with only locals who were willing to converse at a basic level (some were pretty drunk though). I just screwed up the grammar and let the locals correct me.
I don't know if you have been to Prague before but it is incredible.
So I would follow chillies' advice, but keep my expectations low. It is all interesting.
Depending on how much time you have, I would also go through the beginner material in our Czech library. I used it to get started in Czech.
You're right. I'm turned off to the idea of phrasebooks because they don't prepare you for the answers you might get to the questions (assuming you remember how to ask the questions).
My expectations are certainly low. My goal is just to be somewhat familiar with how the language looks and sounds. Time to start Czech here.
The reason I recommend a phrasebook for Czech is because there is so much grammar to even say some little thing correctly. That's why I found it easier to just memorize whole sentences (and still do). I tried to study the grammar for Czech and Polish while I was there and ended up always falling asleep. (But if you love grammar this won't happen to you). If you want to build your own sentences, like I said the locals will correct your grammar for you. If you want a beginner's grammar book showing the general rules for declensions, you can buy one one here, as well as vocab-based books, etc. http://neoluxor.cz/pobocky/palac-knih-neoluxor/ It is right in the center and I'm sure you'll walk by it at some point. Just beware books at this store aren't cheap. You can buy some used books much cheaper in the US. This one is fifty cents. http://www.amazon.com/Czech-Teach-Yourself-Davi... Or http://www.amazon.com/Czech-Lonely-Phrasebook-R....