In reply to lcon:
I've not done anything closer than Mittenwald so can't really help, other than to say that the Swarowski experience is naff - it's basically a series of art installations using their crystals, and the majority of those aren't of any interest whatsoever unless you're into art. The shop at the end was better. The guided tours of the skijump are worthwhile if you can get them in a language you understand.
HTH, and good luck!
EDIT - Saturday, Train to Mittenwald at 08:38, arrives 09:35, return at 18:25 arrive 19:23. Two lakes to the west of town. No idea what the walk is like, but Komoot says it's 10km round trip to the Ferchensee, 'easy' and takes an 'athletic' person 2h 20. Alternatively, the easy Mittenwalder Hohenweg to the east of the town has amazing views if you have VF kit. Descent via the Brunnstein hutte is hard on the knees, might be better to do the VF in both directions and use the cablecar up and down if your knees aren't great. https://www.bergsteigen.com/touren/klettersteig/mittenwalder-hoehenweg/ Not sure about a hut for lunch, there's one without accommodation at the southern end iirc
Post edited at 11:22