Ice skating is not so common in the cities. Although, Vilnius has to offer that.
There are few places for ice skating arenas in Vilnius:
1. Akropolis. A lovely indoor ice skating arena just inside a shopping mall! Great place to hang around, shop & do some ice skating here. You should not worry about shoes / everything can be rented in one place.
2. Pramogu Arena. A whole complex of ice skating, concert arena, with a fairly low price of 15 Litas / 4.4€ per one session per adult.
Both options are around 5 km from Vilnius Old Town and can be easily reached by car. If You wish to use a public transport, click on directions here.
Have fun!