I spent many of my childhood summers in Bavaria, and there are a few things I always enjoyed.
1. As mentioned, going up to the summit of the Zugspitze on the cog-wheel train. There will be snow at the top, and there's an outdoor observation terrace, etc.
2. The
sled track on the Blomberg close to Bad Toelz. Always a highlight - but I can't find an English website.
3. The
Alpamare waterpark in Bad Toelz - great for kids.
Bad Toelz is about 60km from Oberammergau.