I don't think I've ever seen a city park with built-in campgrounds before, but Freeman City Park is a good template for anyplace else that wants to try it. With about 10 or so drive-in/pull-through sites, you can enjoy the amenities of a pleasant city greenspace while also enjoying the outdoors. 

The camp sites feature electrical outlets and picnic tables, but fires are limited to a few grills placed around the park and picnic pavilions (no fire pits).

The park features a playground for kids, two volleyball courts, picnic pavilions, a tennis court, and pool (closed for the fall).

As an added bonus, the toilet building not only features plumbing, but showers!

At $10/night for electric sites and $6/night for non-electric/tents, it's a pleasant little oasis if you need a break from full wilderness camping.