When I was in Munich I stayed at Tryp Munchen hotel for a very reasonable fee (I believe it was around $50 a night. It was clean, updated, and comfortable. They also offered a nice breakfast.) It was just a couple blocks from the train station and about a 10 minute walk to the city center.

I would definately recommend Neuschwanstein. Personally I took a Greyline tour, which included a stop off at Oberammergau, as well as Linderhof Castle. Oberammergau was chock full of hand crafts and gifts at very resonable prices. My cuckoo clock was over 100 euros cheaper here than within the city. At Neuschwanstein, for around 5 euros you can take a horse drawn carriage to the top if you don’t want to hike it with the child. Also as previously stated, Dachau is nearby and worth the visit. Enjoy!