Prague is awesome, definitely has the "traditional european city" feel to it. The beer is awesome, the % on the glass isn't alcohol though, it's gravity. The beer is tasty though....actually where is it not?
Again really depends on what you are interested in but there are plenty of:
-Castles
-Obviously go to "old town"
-churchs, other religious crap
adventure type stuff:
-they have mountain bike rentals nearby and you can go to one of the nearby national parks/protected areas. It's beautiful and you'll come across some traditional villages where no one speaks english
-There is a shooting range outside of the city where you can fire some badass weapons
-I believe they have an indoor skydiving windtunnel but I didnt get a chance to check it out myself
It's a bit of a hike but if you are motivated enough on Sunday you can take a train to one of the other nearby cities like Bratislava as well. Might be about 3-4 hours if memory serves though so it would take your entire Sunday.
Since you mostly just have evenings I would just try to find some local shit to do and always goto a new restaurant/bar. Look for places off the beaten path and get out of the tourist area....though have at least 1-2 nights of fun in Old town
One thing I recommend, and yes I do it myself too, is to go on a "food tour" of every single city I visit/live in/whatever. I do this for a few major reasons.
1.) I love food and drink, worst case scenario I get to eat and maybe find a place to go back to later for lunch or dinner
2.) They usually take you to places in the city a bit out of the normal tourist area, though they typically hit that too. For instance in Sweden(stockholm) we started off in the middle of no where in the residential districts but ended up in their version of "old town". It's a good way to familiarize yourself with the general city layout, learn a little about the area, find some neat markets/places, and again...eat and drink
3.) Most of the time its couples and strange folks, but I have met cool people on some of them. Even the ones where it's just couples/families they tend to be friendly enough. Surprisingly it's not all Americans, it's usually fairly mixed, though that may depend on tour company. I've made drinking buddies and even been on a date from one of them. Also found my apartment in Oslo that way!
4.) You can usually do it after work one night, I prefer one of my first nights in the city. This sort of helps you get your feet on the ground right away