Before you go riding (or buying) try out this cool motorcycle ergonomics simulator.
The Three Sisters (AKA The Twisted Sisters): Ranch Roads 335, 336,337a. A ride through this part of Texas will most certainly change your view of the state. You will ride among scenery as good as it gets, along clear rivers, through very twisty mountain type curves amidst real Texas Ranches. With million dollar vistas and cool clear waters along with friendly folks and knowing that you are riding the best this large state can offer, makes for great riding.
Lime Creek Road: Recommended for advanced riders only. This ride includes tastes of some of the best riding the Austin area has to offer. Lime Creek Road is tight and twisty with lots of hairpins and great Lake Travis views. It also has quite a bit of traffic so you have to stay very alert! As the ride progresses to nameless road it open up a bit with some nice straights mixed with some 90 degree bends. Then on to 1187 which goes through a Balcones Canyonlands, some nice views and elevation changes here. Then onto the classic, 1431 road. This bit near Lago Vista is pretty but other sections of 1431 are more beautiful, but its a great taste of a good road. The ride includes it all and can be done in about 2 hours with spirited riding, so maybe plan 3 to relax with it. There are tight hairpins, open road and beautiful views. The Texas Hill Country is a great place to ride.