If you're wanting to see some sights along the way, then here is a couple of suggestions for Texas; Just south of Amarillo, near Canyon, Texas, is Palo Duro Canyon. It is the largest canyon in at least America, second only to the Grand Canyon. I believe it is a Texas state park, and it is beautiful. Go North to Roswell, then to Clovis, NM, which I remember to be a junky little town, then up US 60 to Canyon, then East on 217 to Palo Duro Canyon. Of course, you're in the middle of nothing in that part of Texas, besides the canyon.
You could go South, making your way over to US 287 and heard south to Pecos, Texas. Not much there, but I think a little history about a judge back in the 1800s. Here you catch US 67 and head SW to Marfa, which is a quirky little town in the middle of nowhere. It's worth a quick look, maybe lunch, take 90 East to Alpine, then 118 to Terlingua, where they have a national chili cook-off each year, then finally to Big Bend National Park. It's absolutely stunning. It has lodging with a nice restaurant that serves good food, or you can camp if you're interested. Big Bend National Park is HUGE!
You could keep going SW from Marfa down towards and then along the US/Mexico border, and you'd ride thru Big Bend Ranch State Park, which is adjacent to Big Bend National Park. The state park is pretty impressive, as well.
After you visit Big Bend, then you could make your way NE towards San Antonio. Just NW of San Antone is the hill country; Fredricksburg, Bandera, Kerrville, Luckenbach, etc. There's some beautful riding in this area, and you'd want to ride the "three sisters", aka "three twisted sisters", which is very scenic and twisty.
"The Three Sisters route starts in Medina, Texas, located 63 miles (101 km) North West of San Antonio. The Three Sisters comprise of Ranch Road 335, Ranch Road 336, and Ranch Road 337 all of them two-lane roads...."
You could then visit San Antonio, which is really neat city, then either go to Austin, or head NE towards the piney woods of East Texas, going thru Bastrop, College Station (home of Texas A&M University), towards either Davy Crockett National Forest, or Sam Houston National Forest.
Just depends upon how much time you want to devote to it.
Supposedly, Ben Franklin said beer is proof God wants us to be happy. So, does my love of beer mean I'm closer to Him?