Oh I would never suggest not going up the mountain. Our first time was on a lovely sunny day, views for miles around. The 2nd time was in heavy snow, coldn't see a thing, still fun though.
What I was trying to say was that your choices for way up/down may be limited by weather conditions. The Eibsee cable car was closed when we went up on the good day, so we had no choice but to take the railway. It was open when we came down. It is very nice to do the round trip.
Definetely add the Partnachklamm is you can. It is pretty amazing. Do check whether it is open though. It was closed, due to dangerous conditions, the whole 4 days we were in Garmisch-Pertenhirchen. It opened again a couple of days later and we drove back from Fussen just to visit. It was well worth it.