Campus View is recently renovated. I've never been in it, but having been redone recently, it should be fairly nice. Tulip Tree, I think, has more people with kids or married couples than any other on-campus housing. The apartments are almost exclusively grad students, although there are a couple of undergrads floating around, so it should be fairly quiet.
The Admitted Student Housing page of the IU-Law website has some information on which landlords allow dogs.
Also check the classifed section of the Indiana Daily Student website, www.idsnews.com
. Look for "grad student discount". Those houses and apartments are often in slightly quieter neighborhoods. Don't be afraid to look around a neighborhood when you find a house, to see if it looks like families live near by. The other area, if you don't mind being outside of walking distance, is about a mile south of campus, near Bloomington High School South. There are some fairly new houses, and it's not a big student area, so it should be pretty quiet.