From Vilnius International Airport some 5KM south of the city centre, the best method of travelling is by bus into the city centre - the short journey to the area where most of the hotels are takes about 10 minutes depending on the traffic.
Touring the country using public transport is cost effective, but timetables for some services can be vague. Renting a car in Lithuania gives you loads of flexibility, and opens up some areas of real beauty. Drive on the right, and be aware that in Lithuania, there is a zero tolerance approach to drink driving, which is strictly enforced.