I would see Carlsbad Caverns and Guadalupe National Park on your way to Tucson. Perhaps a day at North Rim of the Grand Canyon. Maybe a day at Page, AZ. Canyon De Chelly is an option. You could hit the Petrified Forest for a couple of hours.
White Sand Dunes National Monument is a good place to see too.

There isn't much in the Texas Panhandle to see or do. Maybe eat at The Big Texan in Amarillo. You pretty much have to eat there once in your life after passing the 200 billboards along I 40. Actually, it's pretty good. I suppose you might go thru Lubbock though and not even really be in the panhandle.

In Tucson, see the Sonoran Desert Museum in Saguaro National Park. Look into Sabino Canyon and see it that is something that interests you.

I don't know that you'd be interested in this, but The Schlitterbahn in New Bransfel(south of Austin) is the best Waterpark anywhere.

Texas is really big and takes a long time to get across it. It does have some 80 mph hwys, most of them are 70 and 75mph. They have a couple now that are 85mph, but I'm not sure where they are.

A stop at Big Bend National Park wouldn't be entirely out of the question either. Big Bend, Guadalupe, and Saquaro are somewhat similar, so you might now want all of those in one trip. They are unique. Guadalupe and Carlsbad would be easy to hit and they are about an hour apart from each other.

Sounds like a nice trip. What are your interests, besides Bryce and Zion?

Lee Ann

The Texas Hill Country around Fredicksburg is interesting. There are some Texas wineries in the area. there is a nice WW II museum dedicated to the war in the Pacific there as well. The LBJ historical site is nearby.
In the pan handle you can check out the Cadillac Ranch near Amarillo and the Palo Duro Canyon State Park is very scenic and interesting with a drive down to the bottom of the canyon.
In AZ the Herd Museum is an excellent window on the Southwest if you go through Phoenix.

Note that the correct name of the town where Schlitterbahn is located is New Braunfels. It's just 30min north of San Antonio. At that time of year, the park will probably only be open on weekends, and the water will be very cold (it's river water). But the upside is you won't have to wait in hour-long lines!

Also note that nobody mentioned anything between the NM border and central texas - that's because it's mainly just empty desert. Not a fun drive unless you like hours and hours of desert landscape.