I don't know about the Northern parts of 16, but from San Saba to Fredericksburg, it is an excellent, gently curvy and hilly ride.
Fredericksburg is just a tourist trap to me. I suppose there are some fine expensive German restautrants there, but I have only eaten at the more plebian places, which were all very mediocre.
A much better choice, in my opinion, would be to eat at Cooper's in Llano, which is just north of Fredericksburg. If you have never eaten authentic Texas barbecue, you will find it to be quite a trip.
Afterwards, if you want to stretch your legs, Stop at Enchanted Rock on the way to Fredericksburg, and climb the dome.