One of those possibilities would be to take I-44 at Oklahoma City down to Wichita Falls, TX, then pick up US 281. This has the advantage of completely bypassing Fort Worth/Dallas and Austin. A situation "devoutly to be wished" in my opinion--especially Austin.
There is an almost free municipal park in Wichita Falls. The commercial Wichita Falls RV Park is an older park, but it's always been a good overnight for us. About 4 hours down the road is Lampasas, Texas and the Boone RV Park. We've never stayed there because on our trips south we have a different sequence of overnight stops, but it looks like a really nice park, handy to US 281.
Four hours the next day will allow a stop at Choke Canyon State Park, Callahan Unit. It will require a few miles off the route, but it's a few miles we always take. We have stayed there many times on our way to the Valley.
A little less than four hours the next day would put you into Harlingen.
There are many alternative routes, but I just give this as one example.
