Neuschwanstein can certainly be very touristic, but I have been during off season and have made it my way ie not choosing to go with the masses. It does have a lot of unique information as noted above. But Linderhof is more the local castle, and most of the tourists I see are German or Austrian vs American or Japanese. Linderhof is also quite small so easy to navigate, although some of the outbuildings worth seeing are up hills etc.

I was last at Linderhof just a few weeks ago and the areas above the fountain was being restored; I don't know how long this project will continue. My tip is that if visiting in summer, early morning as possible is a wonderful time to visit as the light at that time of day is most stunning.

As to Mittenwald - my family has vacationed there multiple times a year for the past four decades, so I know it well. It has some pleasant gardens, quaint village, and some easy as well as more challenging walks and hikes. It is close to Innsbruck and even Italy - I often cross the Brenner just for a gelato and an espresso.

I echo the Zusgspitze recommendation, however the thing to be concerned with is the changeable weather. If the clouds are low the view is severely restricted and can lead to disappointment. There are sites to estimate the best time of day to visit.