Trains from major destinations come to the Vilnius Railway Station which links Moscow to Warsaw or Berlin.
Jonava has a bus station. From there you can reach Kaunas, Vilnius, Alytus, etc.
The bus ticket for one time costs about 1.20 Lt. You may also catch a private bus, it is actually a bit faster. There is a 50% discount for the tickets for students and elderly people. If you need get there fast, you may catch a taxi, which may cost 4-5 litas. A regular cab may cost about 4-10 litas.
There is a nightclub Banga. The concert hall is in Jonava culture center.