I do the three sisters with as many of the surrounding roads as possible.
Here is what I would consider "must do" roads in that area in addition to 335, 336, and 337.
16 from Fredericksburg to Medina
187 from Utopia north to 39
39 into Ingram
1340 to little stonehenge and on to 41 then circle back to Mountain Home
27 back into Ingram
North of Fredericksburg catch 965 past Enchanted rock
1323 Willow City
then south and east of FB on;
470 Bandera to Utopia then 1050 west of Utopia
that whole area is just chocked full of great roads; just be careful of other bikers thinking they are the only ones on the road and crossing over center lines.
This is a very good list and will give you lots of riding. I'd stay in Kerrville as it is close to most all of this.
I recently stayed at Americas Best Value Inn in Kerrville and it was a nice quiet place located close to places to eat and was clean, comfortable and a very good price.