(a) I haven't been there but the closest to OKC is probably Wichita Mountains Wildlife Refuge near Lawton, where there is an area for backcountry camping: http://www.fws.gov/southwest/refuges/oklahoma/wichitamountains/
(b) It would be about 3 1/2 hours or so to the Lake Fort Smith TR for the Ozark Highlands National Trail, where you could do an out-and-back.
(c) About the same distance to Talimena State Park in OK, where you can start the Ouachita National Trail as an out-and-back. There are 2 detailed books about each of the National Trails above by Tim Ernst, which you can get at Backwoods.
(d) You could drive to the Black Kettle National Grasslands, near Cheyenne, OK.
(e) Maybe too far, but Black Mesa in the far corner of the panhandle is the highest point in OK. Depending on your children's ages, this might be something to look into.
All the above will have websites that might be a good place to start, or stop by Backwoods and ask there.
Edit: Luke beat to it!