I grew up with Tyler in my backyard (literally)
Tyler is great for everything from walking to horseback riding. The park is beautiful and there is even a hostel where you can stay. We run, bike, and rollerblade there as a family. The park is quite large so if you want a quieter area you can find it. You can also fish there. I’ve run a half marathon in the park which was challenging and beautiful. Make sure to visit the covered bridge.
This is one of my favorite state parks. There is an abundance of trees to help keep you cool in the summer. The lake is very clean and there are boats to rent and plentiful fishing. There are MILES of trails to explore from easy to quite challenging. Take the time to get the kids out into nature.