Grünkopf (1,588 m) is a small peak that can be easily reached from Mittenwald. It offers great views of Karwendel.
Ascent: The hike starts from Mittenwald to Leutaschklamm (no entrance fee to the klamm). In addition you can get to the waterfall (3 EUR entrance fee per person). From the klamm follow the easy signed post to Grünkopf. The trail goes through the border. There are no technical difficulties but you should be fit do do 750m elevation gain without problem.
Descent: You can continue on the ridge by following the path to Ferchensee, where you can also take a dip in the lake. From there easy road to Mittenwald.
Weather: https://www.wetter.com/deutschland/mittenwald/DE0007015.html