I keep my bikes in the basement, which has a door that goes outside. The door should be pretty secure, but I keep them locked to the steel basement support posts. The fiancee only lets me keep a bike in the house in one of two scenarios: 1) I'm working on it or 2) it's winter and it's mounted on my trainer.

If I were you, I would definitely keep it locked up--especially given the break in next door. Putting an anchor in the floor sounds like a good idea to me.