Flagstaff Parks: Ponderosa Trails Park

A great park to take small children is the Ponderosa Trails Park (3875 S. Wild West Tr), just behind the Mountain School (map).
This park has a giant soccer field to run and play plus a nice playground, four swings (two baby seats, to regular seats) and a picnic ramada. There's also a portable restroom in the summer months in case potty trainers need one "now."