I studied in Warsaw for 6 months... cool city with hardened, but generous, people. As a person who loves running, beer, and hates museums and general touristy things, I have some suggestions:
I second the Uprising Museum (again, I hate museums but this is worth it). Really powerful stuff and will give you a very good/quick idea of the history of the city and the absolute hell that was WWII for them. Since you're on a time crunch, I'd suggest just stopping by to check out the 20-30 intro video they show. Shows how Hitler turned the city to absolute rubble and will make the city you see now that much more impressive. It's right in the Stare Miasto (Old Town), so you won't be going too out of the way if you're in the big touristy spot.
Also check out Lazienki Park. Big beautiful place to get a quick run in and you'll see some orange squirrels and terrifying peacocks. The "Palace on the Water" is nice to look at for a few minutes as well.
You'll see the giant Palace of Culture and Science (aka Stalin's Penis) downtown. Not worth going up to the top as the building itself is the most impressive thing about the skyline. Take a stroll through the underground market near the metro stop here for some good people watching.
Other than this stuff, I'd suggest finding a nice hole in the wall pub and have a good baltic porter. Also try some zubrowka vodka as well. I hate liquor and especially vodka, but this is different from the stuff we're used to around here (though legend has it the vodka gets its distinct bite from Bison piss on the grass within the bottle).
I have some good pub suggestions if you actually take me up on any of this advice. Have fun, na zdrowie