Staying in Leuven was suggested to another traveler. Any suggestions there or how can I find something there? We stayed near the airport last year and spent too much. I don't want to make the same mistake. We will have a car, but our flight is in the morning.
If you wish to stay near the airport, there is a hotel right across the road...a Sheraton, I believe. I stayed there for a night and was quite pleased. I don't believe that its prices were out of line at all.
Leuven would be ideal if you are using public transportation. Unless you're accustomed to driving there, however, it can be very confusing in a car. Not directly adjacent to the airport, but nearby, there's a number of inexpensive, international chain motels. Nothing too fancy and they're located along an absolutely charmless street, but very convenient if you have a car. Try Googling "Brussels airport hotels".