Any lodging recommendations for LLano or Fredricksburg?

There are a thousand choices for Fredericksburg. I've used this site in the past to find something: https://www.absolutecharm.com/.

Seems like it comes down to staying in Fred or outside of Fred depending on your desire to do stuff in town. In town, we've stayed at this place several times and always enjoyed it. It's on one end of Main Street and you can walk to pretty much everything from there: https://www.thelodgeabovetowncreek.com/

Here's a site with wineries in the region: https://texaswinetrail.com/wineries/

We had a great time at this house just off Main. It's a bit of a walk to most of the shops, etc., but it's doable.

https://www.vrbo.com/9486852ha?