Currently studying in Prague so I've got a few tips:
- For non-touristy sights even though it's going to be very chilly, go up to Vysehrad. Fewer tourists go there but it's the site of the oldest known settlement in Prague and has tons of history, plus the best views of the city. Better than from the castle because you actually see the castle.
- For food, generally stay out of Old Town because it's crazy expensive and not that good. Find any beer restaurant "Kozlovna" or "Pilsner" restaurant, they usually have hearty Czech food for low prices. In terms of beer, ask for local breweries (my favorite place, Hostinec U Tunelu, carries really obscure brands but reservations there are hard). Never ask for Staropramen, the locals hate it and say it's the worst beer. Good bars with lots of beer on tap are the Beer Museum and Beer Geek.
- My favorite place to go watch games is at Rocky O'Reilly's, although they usually show mostly the bigger games. Watched the last derby there with a friend (he's a Chelsea supporter but otherwise he's ok). Bar full of United fans - made it even sweeter when we won. :D