Camping by Transit Gem!
This is the campground we took our oldest daughter to on her first ever camping trip in summer 2015 - so my review is based on the campground as it was in 2015.
We live car-free but we still really enjoy camping, so we searched for a place we could go camping without a car. Barton Park was by far the winner! We were able to take a city bus there and walk the 3/4 mile into the campground - also the fact that they sell firewood and have a store 3/4 mile away was a big bonus for us.
The camping sites were perfectly fine - although I wish there were some walk-in ones that weren't right on the campground road. The playground was being replaced when we were there so I don't know how it is - but I'm sure it's fine. There was a large field for playing in right in the middle of the campground which was nice.