Highway 16 between Fredricksburg and Llano is not bad. I bet there's quite a few good driving roads out in the hill country but I'm not very familiar with the area.
just north of Austin from Round Rock to Marble Falls on 1431 That will give you white knuckles. Similiar to driving the 101 from Carmel down to L.A. not as slow as the road to Hana in Maui with its 600 turns in 52 miles. In Marble Falls there is a greasy spoon called the Bluebonnet Cafe, a must stop and eat at. about a mile south of Wal Mart and Home Depot on the left. if you are there for lunch there is an awesome TEX MEX restaurant just north of home depot. driving south back to Austin and Bee Cave you will pass thru Johnson City. The birthplace home of LBJ is adjacent to Pedernales Electric. intersting stop. and if u make it down to Fredericksburg, beef jerky and polish sausage is the specialty. Lots to see and do in that part of Texas