It really depends on what you an your kids are like. If you're really outdoorsy, you should look into homes in the rattlesnake area (some are more kid friendly then others) because of immediate proximity to hiking. There are also several really great schools out there, both private and public, and it offers up the best public schooling in Missoula based on school zones.
Another really great area for kids is on the slant streets near Rose Memorial Park. This neighborhood also is part of the best public school zoning that missoula has to offer (it jumps around a but based on area), and is packed full of families with kids. Its a great area. These are the only two locations we would move to if staying here, and i've been here 13 years so I know Missoula well.
My guess is that a lot of people would also recommend the university district and especially the U district near bonner park. This area is good too, same school zoning, but is high in price due to location, so that alters who lives in your neighborhood, and does have lots of car and foot traffic for residential streets because of the University. Lots of people will park on those streets unless they require a parking pass. Also, if you look at this area, be sure to stay away from the greek university housing. They can be loud and have frequent parties. We're aren't a college known for it's drinking, but where there is college, there are young college goers looking to party.