Well, first of all, I would swing a bit west and visit the Texas Hill Country, probably Fredericksburg and/or Kerrville. I would avoid Austin unless you really do want to visit our state capitol, but you could include San Antonio unless you have recently been there.
The bluebonnets are expected to be early this year and that would make a visit to the Hill Country especially desirable. We always stay at the KOA out of Fredericksburg.
From there you could go on up to San Angelo or over to Abilene. There are many good state parks where you could spend a day or two along the way, such as Brownwood, San Angelo, Abilene; and up nearer to Amarillo: Caprock Canyon and Palo Duro. March should be a great time to visit any of them.
