You can't get better frugal fun than a library and a park, right? And in Norman, you have the public library right across the street from Andrews Park, which features a splash pad (perfect for a hot day!), a playground and a bandshell (plus picnic tables, shelters, a gazebo, jogging course, restrooms and amphitheater).
After jumping around in the cold water of the splash pad (the kids even complained that they were cold in the wind! To which I replied: "that's not wind, darlin'; this is Oklahoma–that was just a breeze."), we took our cooler over to the stage of the bandshell for a picnic lunch. The stone seating area made for a fun location for an impromptu game of hide & seek after we were done eating. It was a bit hot for the park equipment this day, but we have visited in the past and the kids enjoyed themselves. Plenty of big trees in the area (though a few were lost in the recent storm last spring) provide shade around the park and make it a very comfortable park.
Hot enough for ya? Head over to the library and you'll find restrooms, refreshments (vending machines with healthy choices), a copy of the new MetroFamily (shameless plug) and a fantastic children's area. Separated from the rest of the library with a wall and close to the main circulation desk, the children's area features live animals, comfy chairs, plenty of toys for active and imaginative play, story/activity rooms, a puppet theatre, computers and oh yeah! Books. Lots and lots of books. The well-staffed children's desk will handily help you find a title or make a suggestion.