If you're an art student I can't think of many better places to go than Prague; you're surrounded by Secessionist & Cubist influences everywhere you go! In your shoes I'd probably look at Zizkov or Vinohrady (they're next to each other, near to the main railway station). Zizkov is traditionally the Bohemian quarter of Prague and has plenty of bars with live music. Unfortunately - like most Bohemian quarters - it also has a few, shall we say "questionable" premises, but they're generally easy to spot and avoid. I've stayed at the Olsanka before now - it's actually a few minutes out from Zizkov (funnily enough, in the district of Olsanka!) but there's a tramstop right outside and it's easy to get to & from. It's one of those huge monolithic Soviet-built places, but don't let that put you off; it's very reasonably priced, the rooms are clean & comfortable, and the service is quite good. Breakfast is a bit institutional - an enormous refectory with a big buffet - but filling, if not exactly haute cuisine! Closer in to town, in Zizkov, you might try the Ariston, though I believe it's not as cheap as it used to be.
Other live music venues (depending on the type of music you're looking for, of course!) include the Salmovska near to Charles Square, the Bordo in Vinohradska (walking distance from the Ariston!) and the Rock Cafe quite near to the National Theatre.
There are SO many galleries - fine arts, applied arts, Cubist, Secesssionst, you name it - that you could spend every day for a month doing two a day and still not cover them all. You really should go the the Modern Art Museum - but it's HUGE, so allow plenty of time!
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