I've read everywhere that Vilnius has a great selection of arts. I finally experienced this for myself at a recent performance of Carmen that I attended.
The Opera Theatre is on Vienolio str. 1, which is conveniently close to Gedimino g. You can purchase tickets online or at the Opera Theatre. Avoid shows that are advertised for children as I've heard that misbehaving is common and can cause disruption.
Local tip: try the hot chocolate- delicious, fudgy, warm, yum.