You can find the start of this route by taking the 79 Loop off of I-90 (East or West, doesn't matter). Almost immediately after getting onto 79, you will come to a yellow flashing light. Take a right (East) and now you are on 2523. If you find yourself on the North side of Del Rio, look for signs for 79 and go south. At the same yellow flashing light, turn left and you are now on 2523. Continue on 2523 until you come to a T intersection. That road will be 377. Turn left and continue on 377 till another T intersection. This road will be Highway 277/377. Turn left onto 277377 and continue. Just outside of the northeast side of Del Rio you will intersect with route 79. From there you have a few options. You can take 79 south (take a left) back to the starting point or you can continue straight on 277 to 90 West into Del Rio.
The scenery isn't bad but its not the rolling hills and spectacular views you will find if up in Hill Country. Mostly open, flat, desert views but still better than highway riding.
There are some great twisties and very few significant potholes. Be aware of the tar-snakes as these can get soft in the Texas heat. Stay away from the edge of the road as floods can weaken them and create a lot of gravel. Favor the center line is possible.
Fill your tank in Del Rio before you start because you will not find a single gas station along the route.
Motorcycle Road Additional info
Great little ride if you don't mind being out in the middle of no where. Very little traffic. Be aware of the wildlife, specifically vultures and deer. I wouldn't advise this ride at night.
I was skeptical - perhaps because I've spent some time now in Southwest Texas and had to track down decent rides. Definitely are some but you gotta find them. So I wasn't expecting much. I was pleasantly smacked alongside the head. For this area, -very- nice ride. Great roads, sweepers if you want 'em, areas you can roll on the throttle if desired, and almost non-existent traffic. And actual green vegetation. Thanks to the original poster - much appreciated.