What are your interests, and how close to home are you willing to camp? We'e always liked going to Cedar Valley, just west of Guthrie, to visit Guthrie, but you could visit Guthrie on a day trip from home.
Lake Thunderbird State Park is just east of Norman, it is a water recreation park primarily, several campgrounds, mostly wooded, and at least one has a few full hookup campsites on concrete slabs.
Great Salt Plains State Park north of Enid is always nice, but most people go there for crystal digging, and that doesn't open until April.
The CoE campgrounds on Kaw Lake are popular for a prairie plus trees experience. You'll have to check recreation.gov for campground opening dates. There are several, they don't all open at the same time, and some get closed for high water.
To the south, Lake Murray State Park near Ardmore, and the Chickasaw National Recreational Area are within 2-3 hours from OKC. What campgrounds at the NRA depend on volunteer help, which starts to arrive about this time of year, so again check recreation.gov for availability.
Most of my camping is north and west of Tulsa (particularly on Grand Lake) but that's out of reach for a 2-3 hour limits. Should you choose Grand Lake, I recommend Cedar Oaks in Grove, which is open year round and gets quite busy this early with snowbirds passing through, so call that one for reservations.
Southeast of Tulsa, several lakes are just within three hours, traffic permitting: Lake Eufala, Lake Tenkiller, Fort Gibson Lake and Greenleaf Lake. The first three have a choice of state parks and COE facilities, and Greenleaf Lake is a lovely little state park at the edge of the military revervation.
I've visited the Wichita Mountains National Wildlife Refuge, day trips from Wichita Falls, but have not stayed at the small campground. It is supposed to be a quite place, which will not be the case for the state park campgrounds on larger lakes, and COE's on lakes, once we get into the weekend party boating season.
I've visited Red Rock Canyon, close enough to the west, haven't stayed there. That gets busy on weekends.
Alternatively, you could make a trip west to visit the Route 66 museums (and other attractions) between OKC and Texas. Oklahoma Route 66 museum in Clinton, National Route 66 museum in Elk City. While either is an easy day trip from OKC, both together are a weekend. There are several RV parks in Elk City, free casino parking with hookups in Clinton, and Foss State Park in between.
If you want to stretch the drive to four hours or a bit more, I recommend Palo Duro Canyon State Park in Texas.
