Here's what I'd do, no doubt:
(although you couldn't drag me with you....I'd probably never want to leave)
Google Map directions from frankfurt to Garmisch, with stops
Rent a car. Head south out of Frankfurt to Heidelburg for lunch and maybe a tour of the castle, if there is time. Lots of good pubs in town (college town),
Head south to Freiburg, the gateway to the Black Forest, from here on is a scenic feast.
Keep going to Titesee and Feldberg. Beautiful area. Great people. The spot on the map is actually a great Gasthaus in Feldberg: Schwarzwaldgasthof Adler (Hotel Adler). Enjoy a meal of local catch wild board and venison, or trout from local streams. Stay at the gasthaus, if there's room, if not there are a lot of hotels in the area (it's a ski town). I've never gone anywhere in Germany with reservations. That kills the fun. Nothing like walking up to a gasthaus at 1:00AM drunk throwing money at a 80 year old woman. They usually feel sorry for you and treat you extra nice.
Next day, head east and enjoy the scenery of the Boden See as you head to Neuschwanstein Castle (tourist trap but worth the trip).
After that, keep going east to Garmisch. Lots of hotels there, tour the Zugspitz just 5-minutes south of town (there's a cable car that takes you to a ski house on the peak).
The directions stop there. Head south to Innsbruck or north to Munich, or both! They're not far.
It's easy to get around Germany with a good map. All the roads go right to the center of each town and roads are well marked. Buy a road atlas.
If using your fingers to show numbers to order beers, remember your thumb is 1, the rest of your fingers are 2-5. If you just show your pointer finger, trying to order one, you're likely going to get 2.