Does anyone has any recommendations for things to see and do in Prague off the beaten track?

There is a restaurant by the river with a good view of Charles Bridge. The access to the restaurant is down a narrow stairway from the street near the Kafka Museum. It's so narrow that there is a traffic light controlling traffic up and down the stairs. Even if you don't eat at the restaurant, it makes a good photo.

The Convent of St. Agnes has an excellent collection of medieval art. If you take the metro to Vyšehrad, the church is interesting but be sure to take the time to wander through the cemetery outside http://www.praha-vysehrad.cz/lang/l2

Personally, I like the National Technical Museum. Great collection, wish I could go again. There are other museums up on that hill.