Is Neuschwagen Castle a good choice?
Sure it is. I would visit Neuschwanstein, but it's 1 hour by car. But it's a nice trip. You can see the Alps and nice lakes along the way. Also you can drive a german highway as fast as you like, because there's no speedlimit on german highways.
A must: Augustiner beergarden in Arnulfstreet. Oldest, nicest, and full of tradition. Best beer brand, you can bring your own food. Many locals are here, like me.
Hofbräuhaus is famous, but a tourist trap.
English garden is a large parc in the middle of the city, with small lakes and again two beergardens (Seehaus on a lake and Chinese tower) Both are nice.
BMW Museum, German Museum, Pinakothek (modern Paintings and sculptures)
Take a trip to the Tegernsee, a nice village on a mountain lake or Starnbergersee. See = lake in german. Both lakes are about 30 kilometres from Munich.
Enjoy your stay in Munich about 6 years ago