Advice on Neuschwanstein/Zugspitze as Day Trips?

I think I'd go with number 3, Diana. I'd take my chances on the weather to avoid all that travel time. Plus I love to stay in small towns, and Bavaria has some beautiful ones. I have not been to Fussen, so I can't comment on that. We visited both of those places from Mittenwald, which is a wonderful town. It is much closer to Zugspitze than the castles, and the location would be almost as convenient as Fussen.

Diana,
Option #3 is truly the best for time. If it is clear the 1st day go ahead to Zugspitze in the morning and then take in Linderhof(which is a small castle) in the afternoon. The next day do Hohenschwangau and Neuschwanstein castles, they are close to each other. Also since you have 6 days, check the weather and then run by the main Bahnhof and rent a car for the days that seem the best weather wise, your hotel could probably help you with this.
Jerry

Let me throw in another suggestion. Stay in Fuessen,see the castles and use 1/2 day for the Tegelberg gondola and a couple of hours at the Royal Chrystal baths. I built in a little down time last year and spent 2 hours at the baths after taking the gondola up the mountain. It was one of the highlights of the trip. Lying back in the hot, salt water looking at the mountains with a view of the castles was amazing. You can get to Zugspitze from here or move on the Reutte or Garmisch and go from there.

I would suggest you stay somewhere on the Ausserfernbahn, Pfronten or Reutte i. Tirol. Both are very close (½ hr) from Füssen with regular bus service and connected to Garmisch-Partenkirchen by rail. Of the two I would prefer Pfronten. It's a nicer town with some nice accommodations within walking distance - no need for a car. I think you can see the Zugspitze from some parts of town. You might consider staying here.
I would have suggested Oberammergau for it's convenient bus connections to both Hohenschwangau and Garmisch-Partenkirchen, but not during the Passion Play, which ends in October.

I'd do number 3. I saw both of these places in Christmas 09, and this seems like the best option. Zugspitze with Linderhof thrown in is a great day. It's a spectacular little palace, and you can spend hours roaming the grounds as well. Neuschwanstein and Hohenschwangau share a parking lot, so they are an obvious day together. I stayed in Fussen with car, drove to the king's castles one day, then drove to Garmische with Linderhof en route. There is no concern about the car in any of these places, as there is safe parking for all places. Don't miss Linderhof, it's really great.

Although you can do the trip by car, it's a lot less expensive by public transportation. A Bayern-Ticket will get you (all 4) anywhere by regional rail or RVO bus in Bavaria after 9 AM workdays, midnight weekend days for just €28. The buses to Füssen/Hohenschwangau from Pfronten or Garmisch-Partenkirchen are completely covered by the Bayern-Ticket. The bus from Reutte to Füssen is only partially covered because it runs partly through Austria. The Außerfernbahn, the rail link between Kempten and Garmisch-Partenkirchen, although mostly in the Austrian Tirol, is run by German Rail, and thus covered by a Bayern-Ticket.