Here's what you need to do. Ride with the traffic on I10 all the way to San Antonio. Speed limit varies from 70-75 all the way and most traffic will be running at 80. Be sure to slow down whenever I10 goes through little towns, especially nearing San Antonio.
When you get to SA, go west two hours on 90. At Sabinal, go north on 127, dip over to 83, and then ride into Leakey. Leakey is the southeast corner of the Three Sisters. It isn't the Blue Ridge Parkway, but it is a great ride--borderline unbelievable for Texas.
Google or YourTube "Three Sisters and Texas hill country." The Sisters takes about two, two and half hours to complete. Reward yourself with a cold beer and cheeseburger back in Leakey, then wind yourself northest back up through the hill country back to Austin. Be sure to look up the Lone Star Motorcycle Museum on your way back to Austin. The Sisters/hill country ride redeems the otherwise boring ride in from Houston on I10. And beats the hell out of anything you'll see on on I20.
2012 XCT White
San Antonio, TX
Honda CB350, Penton 125, Penton 175, Honda MR 175, Honda TL250, Yamaha IT 175, Husky 250CR, Husky 360 Auto, Husky 390WR, BMW R90/6, Honda CX 500, 84 Goldwing, 93 Goldwing, 98 Goldwing, 2012 Victory XCT