David,
We live in Prague as well as the UK so some further suggestions.
Fotoskoda (already mentioned) is a great shop with a large selection of s/h analogue cameras and new equipment. They also have a book section with a good range of Czech photog books. They are very centrally located, just off Wenceslas Square. I also use BeFoto, a small family run traditional camera shop in Prague 7. Their equipment and film prices are the best in town. Recently bought all my B&W darkroom equipment from them.
Re galleries, the Prague City Gallery - House of Photography is good and centrally located - In January they had a great Sam Shaw exhibition. Also the Leica gallery (a bit small but has a cafe and a bit of a photog book library). Also, check out the DOX gallery - is is a modern art exhibition place with a great book shop and sometimes has some good photo exhibits.
For interesting places - there is so much - We have lived in Prague for over 5 years and still are finding new places. I like the Prague 7 District, it's former industrial, gradually being gentrified with the Prague harbour/marina and Letna park within it. Really depends on what you want - street/people anywhere in the Old Town or Mala Strana (Lesser Town). Industrial (old, new and decaying) look at Prague districts 4, 5 and 7.
Authentic Czech food - great beer is everywhere and I find food can be a bit hit and miss.
Have a great trip and PM if you need any more details.
Peter