Within a 2 hour drive of Dallas:
Tyler State Park, Lake Tawakoni State Park, Lake Ray Roberts State Park, Cedar Hill State Park, Glen Rose State Park, Cooper Lake State Park.
I haven't explored the area around Lake Ray Roberts so not sure how much is there to visit, but the park is nice. All of the other parks are nice but also have nice areas around to visit. Except for Cedar Hill, think small town and cool Mom & Pop stores.
3-5 hours from Dallas:
Fort Griffin State Historic Site. Haven't been in 2 years since they did some updates, but it is a neat historical site. They were supposed to update the campsites and then my DH changed his dove lease to a different area. Hope to make it there after DD graduates and my time constraints change.
Copper Breaks State Park. Again neat historic campground.
We also enjoyed McKinney Falls State Park in Austin. It is in the middle of Austin, so we really used it as a hotel for sightseeing.
As you can tell, I'm a state park geek. We buy the state park pass and get our money's worth. And I love to visit the areas so I'm not necessarily looking to hike and bike all the time. We enjoy just sitting around the campsite and chilling out. And yes, I'm the type to stay inside sometimes and watch tv and do my camping crafts. My DH uses the campsite as homebase during hunting season so we spend quite a few winter weekends out.
We've spent several summer vacations down at Galveston Island State Park, but it's really starting to wear waiting for them to rebuild after it got wrecked a few years ago.
Enjoy your new adventures!