Some ideas..
Hi Gary,
Hilltop Cafe - (830) 997-8922 - on Hwy 87 about 10 miles NW of Fredericksburg. It's a German/Cajun (husband/wife) restaurant out in the middle of nowhere. You'll see folks dressed in their Sunday's best to very casual. If you like German Chocolate Cake, best you call ahead and reserve a piece. The husband is into Blue's music and he'll sometimes come out and strike up a tune. Probably also a good idea to call ahead and reserve a table.
Willow City Loop - If you're in the mood for a small road trip and a nice sampling of the Texas Hill Country, then this is pretty hard to beat. It's best in the springtime when the Blue Bonnets are in full force. We've had drought conditions for quite some time so it's probably not in its best form, but still a pleasant tour. Take Hwy 16 North about 13 miles, then right on FM1323 (the FM stands for Farm to Market) towards Willow City for about 2.7 miles, the left on Willow City Loop. It'll eventually come out on Hwy on 16 - just turn left to get back to Fredericksburg.
No doubt that Coopers BBQ in Llano is great. If you'd like to take a less common drive to get there, Take Hwy 87 North for about 8.5 miles, then turn right onto RR2323. This'll take you right into the south side of Llano. Turn left on Hwy 16, cross the Llano River, then left on Hwy 29. Coopers is about .5 miles on your left. To get back to Fredericksburg, just get back on Hwy 16 south and that'll take you straight back.
If you're into historical sites, LBJ's ranch is "just east of town" on Hwy 290 by about 17 miles.
If you're into the casual of casual and motorcycles, there's Luckenbach, TX. Head east on Hwy 290 about 5.5 miles, turn right on RR1376 (the RR stands for Ranch Road) - there's KOA on the corner if I recall correctly, then head about 4.5 miles on your right.
Welcome to Texas!