I grew up in Gainesville, TX. (6 miles from the Red River) we used to go up into OK to Lake Murray and Turner Falls, + the Davis area a lot, as well as Lake Texoma on the TX side. Lake Murray State Park is nice, OK does not have very many State Parks, but the ones that they have are very well done and maintained IMHO. Sulphur, OK just east of Davis has a great park to ride bikes in. It used to be named Platte National Park, the smallest Nat'l park in the US system. Lots of great places to take the family for summer fun within an hour + of you. There are a lot of little towns to explore off 377 in OK. Just be sure to drive 25MPH thru the little towns with that front TX license plate!
You should also consider the lower SE corner of OK. around Broken Bow, since you live about a 3 hour drive from there. If you go up there, Beavers Bend State Park is a great place as well as Broken Bow Lake. Highly recommended for a great place to stay very close to Beaver's Bend and the lake is
http://www.pinemeadowcabins.com/ Tell Doug and Dian that I told you that you must be treated right!
They are great people, and have some awesome cabins, for family stays, and especially if you leave the monkeys for a couple of days! :wink: They have used a few of my pictures for their web site in the past.
One of our favorite car day tours up there is the
http://www.talimenascenicdrive.com/. Fantastic in the Fall colors! It's about 30 minutes north of Broken Bow.
edit: (Feeling like I work for the OK chamber of commerce, but
If you would consider traveling a little further (about 5 hrs from you) OK has another surprising mountain range to explore. It's about 30 minutes north of Wichita Falls, Tx.
http://en.wikipedia.org/wiki/Wichita_Mountains. Living on the west side of the metro mess, we do WWR in a long day, but you should probably plan at least one night overnight stay. We especially love the hike up Elk Mountain, and the hiking trails thru Charon's Gardens area. Drive up Mount Scott for the sunset.