Just walk around the old town all day, I guess... I'm in it at the moment, but I won't be doing much out, maybe visiting a lecture but that's for local speaking blokes.
Get a transport card (10 days pass), peep it once against the yellow block inside the bus/trolley. You can climb up Gediminas Castle, or nearby hill of Three Crosses for the panoramic view. Go to Archicathedral square, then to see the church of St. Ann's (Sventos Onos baznycia). Nearby is small area called Uzupis, you can pop in, although not much to do in this weather but get in pub.
I'm not a party person, there are sure several clubs, but you'd be better finding them yourself... They're located in the old town for the most part, anyway.
can try this website