Going to Venice sounds like a good idea. The train usually takes about 2 hours from Verona to Venice. For more details you can visit the website of the Italian Rail:
http://www.ferroviedellostato.it/
My other advise would be to get a rental car and drive around the Lago di Garda which has lots of great scenery and quaint little villages.
Verona itself is a pretty nice city with lots of historic sites including the Colosseum.