We like to base out of Kerriville simply because it is in the middle of everything.
All the chains are represented as will as the YO ranch resort and Inn of the Hills. We just got back from a 4 nighter and stayed at the Comfort Inn & Suites.
Fredericksburg, Tx has some very nice older places in and around town, expect to pay a bit more and it is not quites so centerally located.
If you like a little more off beat, try the Koyote Ranch (they have cabins, a general store, small grill and camping) they are half way between Kerrville and Medina on Hwy 16 and very motorcycle friendly.
The D'Rose Inn in Leakey is a 2 wheel only resort and is nice.
This does not even scratch the surface, others will chime in with their favorites. There are B&B's, Cabins an all sorts of other things to be found in the Texas Hill County, ya can't go wrong.