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.
This campground is a strange hidden gem - stick with me through the downsides. Taidnapam is on Riffe Lake, which is created by a dam and as of about 2013 the water levels have been permanently lowered by 30-ish feet. This is bad news for people who only went there for boating and fishing and swimming in the swim area but for some of us it's actually good news.
The campground is slower than it used to be during the summer months due to the lowered water levels - but that means you can often still get a reservation at the last minute, especially for the walk-in tent sites (which is what we use). We have camped for three years now at the walk-in tent sites and it's a bit tougher to access the water but you definitely can still find plenty of places to get in or take a kayak down to the water. There's also lots of fun areas around the edge of the lake to explore that used to be under water - making for interested hiking.
We love this campground to go to with kids - the walk-in tent sites are great and the water is so shallow now for quite a ways out so the kids can play in the water and the sand/mud along the edge of the lake. There are so many nooks and crannies around the edge of the lake to explore with the kids - and we used an inflatable kayak while there to go across the lake. They also have a scavenger hunt of items hidden around the campground that you can do with your kids (or if they are a bit older they can do on their own) and a playground.