The capital and the largest city of Lithuania, Vilnius is home to over 550,000 Lithuanians. It is a very common travel destination, especially for budget travelers because of the great value it offers (as in all of Lithuania, it is very inexpensive to visit Vilnius). Vilnius is an old city, dating back to the 13th century.
Vilnius has its own airport and is also served by many bus and train lines. Nearby city Kaunas is served by the no-frills airline Ryanair, and Vilnius is a 5.5€ bus ride away from there. Flying into Kaunas and then taking the bus to Vilnius is a very common and inexpensive way to get to explore the nation's capital.
Most hostels in Vilnius are concentrated close to the main city area, especially the older parts. The city is easily small enough to travel by walking. Vilnius hostel prices are very affordable, starting from as low as 10€ a night for a dorm bed and a bit more for your own room (or a double/ twin). The old town area is really beautiful and you can easily spend a whole day just walking around, enjoying the shopping, cuisine, and sights of this old city.
There are some things most people see and do when they stay in a Vilnius hostel. One of them is the Museum of Genocide Victims (often referred to as the "KGB Museum"). Gediminas Castle (on Gediminas Hill) and the Vilnius Cathedral are also famous sights and well worth seeing. If you're interested in theatre, you will really enjoy Vilnius (like most of Lithuania). Be sure to check the Lithuanian Opera and Ballet Theatre.