I will be in these two cities for a week and would like to find some places to eat/drink where the food is good and it might be possible to strike up a conversation with the locals. I'll be by myself. Any suggestions?
Last time I was in Prague, I was a little depressed by the sheer lack of locals in most of the restaurants. But one places where actual Czechs can be found:
Restaurant U Medkidku, on the corner of Ulitas Narodni and Na Perstyne. Odd, the bar was full of obnoxious American frat boys, but the restaurant's patrons were primarily Czechs and Germans. I don't remember the name of the other restaurant, but Rick lists it in his book... or at least, he did last time I consulted his Eastern Europe book in 2005. Its located nearby on Rytirska, and has a similar ambiance and menu. I'm pretty certain that I and my companion were the only Americans in the restaurant. Rick describes the neighborhood as a "red light district", but I'm not sure why.
I can't promise you'll get into conversations but your best bet, and some of the nicer eating places in Prague, are out of the centre (not surprisingly.)
I like the area around the TV tower, which can be easily reached by taking the metro to Jiriho z Podebrad which is a couple of stops up from Museum.
A favourite in pub in this area is U Sadu at Skroupovo namesti 5, Prague 3. Cheap beer, good food and the best pickled cheese in the area.
The restaurant opposite the front of the church on Jiriho z Podebrad Square is also worth a visit. Name escapes me at the moment, but I think it also contains Sadu.
I don't know it personally but ex-pat friends in Prague say U Zpevacku, Na struze 7, Prague 1 is a good place to meet other ex-pats.