Probably nice for information: inyourpocket.com, there are also apps in the Apple and Google app stores: "In your pocket City Essentials". (Found via booklet in eLoftHotel)
Kernavė: A village far outside of Vilnius and the first capital of Lithuania (or so I was told). The village is now a state culture reserve. It is accessible by bus from the bus station. (Info on the website of the tourist office) (Kernavė's own website)
BIX Baras: Cheap. Also profiles itself as a beer keg, but actually the beer list is very limited and the quality of most beer is rather mediocre. The food is more than OK considering the low price.
In the Vingio park there is a cruising zone (54.686214, 25.239284), but it is not very comfortable due to the many insects.
An area along the Neris upstream from the beach of Valakampiai (54.730418, 25.295281). In good weather on weekends, this is a very active zone. Men sunbathe naked in open places between the reeds, although there are also those who simply sit along the small paths. Leave the paved path past the normal beach and stay as close to the river as possible.