I've got a couple of places I like to stay, but I always take 412 across Arkansas, Oklahoma and New Mexico, and that's probably way too far north of I-40 for you.
If you're up for exploring, they are Keystone Lake, near Tulsa, Fort Supply Lake near Fort Supply, OK, and Maxwell Wildlife Refuge near Maxwell, NM. I've also stayed at Lake Meredith near Fritch, TX a couple of times. Keystone Lake is the only one of those that you have to pay for.
I've also over-nighted at the west bound rest area west of Cline's Corner on I-40. The "watch for snakes" signs aren't kidding. I almost tripped over about a 4' rattlesnake there one time.