Lived in Vilnius for two years, and I love it. I'm so jealous when someone says they're going. That said, I'm not much of a clubber, so I don't have a lot of personal experience in that regard - but I can give you a couple of thoughts.
First up, when you arrive, pick up the latest copy of Vilnius In Your Pocket. You should be able to buy one right at the news kiosk in the airport arrivals area, en route to the taxi ranks. (If you call for a taxi in advance, it's cheaper than just catching one from the queue, but it's still relatively cheap for a ride into town - should be around 30 Lts or about $10, though I haven't made the trip for more than a year now, so don't know about inflation. Getting around by taxi in town is really cheap if you call ahead, much more if you just flag down a cab.
The list of bars/clubs in the IYP is pretty extensive, but there are also lots of small pubs that often have live music - Arklys on Vokeciu is a good venue for jazz, and Markus ir Ko (in Zydu g.) often has live music too. I can't remember the name of the place next door, but if you sit outside, you can listen to the music from Markus ir Ko while having a student-budget meal. We went a couple of times with my husband's classmates, it starts with an "A". If you continue down Zydu g., you'll come into a courtyard with a statue of the Gaon of Vilnius, a noted Jewish scholar, and will be in the WWII era Jewish ghetto. There's an interesting display discussing Jewish history in Vilnius near the entrance to the playground across the street. The Jewish population of Vilnius was in the neighbourhood of 250,000 prior to WWII. Afterwards, it was down to 5,000.
As you're looking at the information board, the brick building behind it (next to the statue) was my daughters' school, so it's very familiar territory for our family.
I hope you'll have a chance to see more than just Vilnius' bars, the city is truly a gem. If you have any other questions, I'd be happy to help.