travel to Garmisch

How long will you be there? Will you be travelling from Munich by train or rental car? Rick's Germany guidebook has a lot of good information, by the way.

Take the cable car to the top of the Zugspitze.

"...any information greatly appreciated Jerry"
Lots of that below:

GARMISCH-PARTENKIRCHEN
The Fraundorfer is one of many places to stay but more importantly the site of "Bavarian Evening" meals with traditional dance and music.

Nearby MITTENWALD
FÜSSEN

The nice way to Füssen from G-P is to take the direct train through Austria on the "Außerfernbahn" route. Then catch the bus into Füssen:

http://www.diesellokguru.de/images/D2014/D2014-4/D965-111-027-2014-04-17-23.jpg
https://en.wikipedia.org/wiki/Ausserfern_Railway#/media/File:Au%C3%9Ferfernbahn.png
https://en.wikipedia.org/wiki/Ausserfern_Railway

I have a couple of suggestions for where to stay.

Oberammergau: there are a number of direct 40 or so minute bus connections from Oberammergau to Garmisch-Partenkirchen every weekday morning at 6:47, 7:35, and 8:35, so you can stay in Oberammergau and get to GaP in time to go up the Zugspitze in the morning before it gets cloudy. There are also 1h20 connections by bus to Hohenschwangau each morning. Gästehaus Richter is a good place to stay in Oberammergau. It's close to the bus/train station, reasonably priced, and Frau Richter speaks good English. Americans visiting the NATO base in Oberammergau often stay there.

If you stay in Oberammergau, you can also visit Linderhof, which is a 20 minute bus ride from Oberammergau, or Ettal, which is 15 minutes away by bus.

To get to Oberammergau by rail, go south towards Garmisch-Partenkirchen, get off at Murnau, and take another train from Murnau to Oberammergau.

Another place to stay is in Pfronten, which is 1½ hrs from GaP via the Außerfernbahn. There are buses from Pfronten to Hohenschwangau that are cost free with your Pfronten guest card. I've stayed at Gasthof Aggenstein in Pfronten twice. Nice place, reasonable price, about a block from a bus stop.

The best way to get to Pfronten is via Garmisch-Partenkirchen.

Look up rail and bus connections on the Bahn schedule and fare webpage, https://reiseauskunft.bahn.de/bin/query2.exe/en

Oberammergau is a delightful place to visit and I strongly suggest you do so even if you do not stay there.

We spent a week at G-P a few years ago and loved it! We stayed at the military installation so I don't have a good hotel suggestion for you other than to state there are many nice looking hotels there. It is easy to get to the Ski jumping hill by local bus and go hike the gorge or take a luge ride. Have rain gear for the gorge. The train up to the Zugspitze is fun and easy to catch. Lots of walking and hiking paths throughout the area.