We are going to be in Munich until Oct 3 and have a few days before we have to drop our daughter off at the airport for a flight on Oct 7. She wants to see Newschwanstein Castle so we thought we'd spend those days in Southern Bavaria.Should we just spend the 3 days somewhere near the castle? Maybe Oberammergau? Somewhere else? I thought we could do the castle, Zugspitze, what else? Or, would i be pushing it to go to Berchtesgaden for 2 days, then go over the Oberammergau, and then head back to Munich? We'll have a car.
Your input is appreciated.

In addition to Neuschwanstein, there's also Hohenschwangau and Linderhof. Some distance away is Herrenchiemsee located on an island in the lake of Chiemsee that can be accessed by boat at Prien am Chiemsee. Garmisch is about an hour drive from the castles in Fuessen and if you buy your tickets in advance, you could at least see the two larger castles in one day. Garmisch is perfect to use as a base for the Zugspitz and visiting other small towns nearby.

I've always preferred Linderhof over Neuschwanstein but I understand wanting to view the more famous site.

I think one castle is enough. My question is whether we should stay in that area or if we would have time to take the Alpine Road and see Bertesgaden and whether its worth it or would it be best to stay near Garmish for those 3 Days

I recommend you to visit Munich then go to Neuschwanstein after this visit Memmingem and return to Munich. Check car rental here https://rental24h.com/germany/company/global-rent-a-car , I used this service when was in Germany, I liked it. If you have more time recommend visiting Stuttgart.

Oberammergau would be a great base or Garmisch, I think you're pushing it to try and see anything else in your time allotment. You can spend all day going to the top of the mountain. Have lunch there for sure. Hike the gorge. Ettal is nice on your way to Oberammergau. The Post hotel there is good to stay in but there are many guest houses also. That is where the NATO school is, many don't know that. I also like Linderhof, the grounds are amazing. The house tour is ok.

I second Macross's suggestion on Garmisch. We just' happened to end up there' by accident a few years ago and loved it. Be certain to hike the gorge though... lots of hiking trails around there as well. Munich vs Garmisch really depends on your preference - large city or smaller with gorgeous scenery. We enjoyed Munich as well but after two days we were ready for hiking and exploring the countryside... your preference. Enjoy ! It is a beautiful country.

Hike the top of the Gorge also, nice little beer garden up there. The Olympic stadium is very historical.

Great advice. Thanks everyone! We can't wait to see it.

Herrenchiemsee Castle to me was really neat - boat ride there - the Bavarian Versailles. Go to Prien and hop ferries.