Missoula's downtown is pretty small, but still has quite a bit to offer.
Caras Park (in downtown Missoula) holds a variety of different events throughout the spring/summer/fall that are usually enjoyable, some more family-friendly than others.
Downtown has some great places to eat, shop, drink, etc.
There are a couple pretty cool bars downtown that have live music.
The Wilma Theatre shows (mainly) indie films, but also holds a variety of events from concerts to film festivals to book readings, etc.
As far as things that are good for families/children, downtown has the carousel and dragon's hollow, which is a little playground/park.
There's also the Missoula Children's Museum on Front Street.
I'm not really familiar with family/children-friendly things since I'm pretty young and don't have a family, but I do know that there are things for families with children to do downtown.
You could always check the Missoula Downtown Association website for more info on events and happenings downtown:
Missoula Downtown Association