You're brave to plan to go to Vilnius that time of the year! Even in the spring, it can be really cold you know, so make sure you take a lot of warm clothes. I like going there in winter particurarly, the landscapes look even better when they're covered in snow There are many places to visit, I can't start to talk about them, the list is endless, but I guess all of the important stuff are in the old town. It's truly beautiful city, I'm sure you won't be bored!
I see you're from Belgium! I've been there a couple of times, I really enjoyed it and thought people were very friendly