Hey, I'm a Missoula Mudder too with wife and two little girls age 5 and 7.
Like Landroamer said, there's a KOA right in town by the REI and Costco. You can tent camp for free on USFS land and there is plenty within a reasonable distance from town. Reasonable distance by Montana standards, that is. Time/distance can be deceiving here.
Within 100 -/+ miles, there are ghost towns, rivers to raft/float, hot springs (commercial and natural), trails to be driven, national forests, all-down-hill bicycle path: the Hiawatha Trail, Lake Como, dirt mountain passes like Skalkaho, which also has the Gem Mountain Saphire Mine, tons and tons of wilderness, and so on.
In Missoula, there is the Carousel/ Dragon's Hollow, Currents Indoor Water Park, Splash Montana outdoor water park, Fort Missoula, Children's Museum, riverside trails, parks, more parks, hiking up to the M, floating the Clark Fork River through town, floating the Blackfoot river just out of town, fishing, music at Bonner Park on Wednesday evenings, and several breweries, etc...
Check out the Special Editions here like "Best of Missoula" and "Explorer".
http://missoulanews.bigskypress.com/
It should be beautiful in July. I would consider one of the camping areas on the Blackfoot river on the Blackfoot corridor. That might be farther from town than you'd prefer though. On Google maps, it's called Johnsrud Park Road as it comes off of Hwy 200.
but regaurdless its a pretty place, 
