There is really no bad areas to definitely avoid. The most popular area for expats is Vinohrady. Lots of bars/restaurants, close to the center and nice area.
Letna is another nice area close to a great park with a beer garden overlooking the city. Popular area with the locals because it has amazing views and the tourists don't know about it. A little longer walk to downtown, but not bad. You can always take a tram back (cheap and safe).
Anything in Prague 1 will be in the very center, which is nice, but likely expensive. Unless you just want to be in the center for convenience there is no need to pay the higher price. Nothing is far away and public transportation is great.
Staying in Letna or Vinohrady will give you a much better feel for the city. The center is more of a Disneyland with little that is actually Czech. It's nice and looks great, but not really very Czech.
Almost forgot. There is a new up and coming neighborhood called Karlin that has been rebuilt after the 2002 flood. Used to be a dump, but is now all new and nice. Easy walk to the center, but make sure you are fairly close to the Florenc metro stop, it is a big neighborhood and being on the far end would be very nice or convenient.
Feel free to ask me any questions, I've lived here for 15+ years. My wife, who was born here, asks me for advice/directions.
