How much time will you spend at the camping areas? I have a few in mind...I'm on the app right now, but once I get to a computer I'll look at your route closer.
*Edit
So depending on how much time you have and how far off I-40 you want to go I'll throw out a couple ideas from east to west.
-Devil's Den State Park, AR.
Its about 20 miles south of Fayetteville, AR. Great campsites, great views, and the Fossil Flats mountain bike trail is a great ride. It's about a 5 mile loop with some cool sections of single track above Lee Creek.
http://www.arkansasstateparks.com/devilsden/
-Wichita Mountains Wildlife Refuge, OK
It's about 60 miles southwest of OKC so a bit out of the way, but probably the best state park in OK. Great hiking and mountain bike trails. Semi-primitive camping and back country camping available. Here is a picture I took when I hiked there in Jan. 2016 to give you an idea of the terrain.
DSC02126 by
DerekG710, on Flickr
https://www.fws.gov/refuge/wichita_mountains/
-Roman Nose State Park- Watonga, OK
This small park is much closer to I-40 (15-20 miles). It has ~12 miles of mountain bike trails......of the ones I have ridden, the loop to Inspiration Point was the funnest. They also have plenty of tent camping sites as well.
http://www.travelok.com/listings/view.profile/id.6460
-Palo Duro Canyon State Park, TX.
It's about 25 miles south of Amarillo, TX. I haven't been here yet, but it is on my short list as it looks awesome. I think it is the second largest canyon in the US, the Grand Canyon being the first. They have lots of campsites and plenty of hiking trails.
http://tpwd.texas.gov/state-parks/palo-duro-canyon
I'm not too familiar with the biking scene in NM and AZ, but I'm sure there is plenty. Santa Fe is a cool place to hang out. The south rim of the Grand Canyon isn't too far out of the way and I hear Lake Mead is a pretty cool place. There is obviously more to do along the route than you could do in a month, but those are a few that I would check out if I were doing the same trip.
