VB Sleep Inn is a great small cozy place to stay in the city center. I really enjoy that place. As it is small and good, unfortunately it offen get's fully booked... Šv. Mikolojaus 3, +370-63832818, vb.sleepinn@gmail.com, online booking.
Old Town Hostel is between the city center and the railway station. Aušros Vartų gt. 20-15, +370-5-2625357, online booking.
Vilniaus Jaunųjų Turistų Centras is in the Už Upis Area. I stayed here 5 years ago and it was nice. Might be an interesting place to stay by now, probably not so full of international tourists. Polocko gt. 7, phone: +370-5-2611547 or 2613576, vjtc@delfi.lt, 34LTL.
AAA Hostel is very close to the railway and bus station, which is a kind of skid row area at nights. They have three places all close together: Sodų 17, Sodų 8 and Šv. Stepono 17, +370-5-2139994, online booking.
Paupio Namai is in the Už Upis area. Paupio 31a, +370-5-2643113, hostel@paupio.lt, online booking.
Filaretai is also in the Už Upis area. Filaretų gt. 17, +370-5-2154627, info@filaretaihostel.lt
If you need a map of Vilnius take Mr Gordonsky's CitySpy Map. Another good source of information is Vilnius In Your Pocket. The official Vilnius Tourist Information is also quite good, or have a look at the official Lithuanian Tourist Information.
As not everybody is speaking English in Lithuania and as you don't want to feel stupid by not even knowing how to say 'Hello' in Lithuanian, print yourself a copy of the Pocket Talk English - Lithuanian micro dictionary.