Please offer your opinion on best of these options for a visit to Neuschwanstein area.
1) We could do a day trip from Munich since we will be staying there prior.
Advantage - No need to change hotels and haul our luggage.
Concern - It seems fairly easy to do via train, but would it be too rushed? How early would we have to leave Munich to do BOTH castles without rushing through them?
2) We could stay one night at a hotel a couple kilometers from the castle (maybe Weinbauer at Fussenerstrasse 3), or
2a) stay at a hotel very close to the castle, like Alpenstuben at Alpeseestrasse 8
Concern about staying locally (2 and 2a) - How easy is it to get around without a car?
Any thoughts would be appreciated.
"How early would we have to leave Munich to do BOTH castles without rushing through them? "
You can only tour the castles by guided tour, and your tickets dictate a set entry time at each. Your tour procedes according to the pace determined by the guide, which is fairly tightly structured to allow for the huge number of people who want to visits the castles daily. So, the time of day you arrive has no relation to how long you can spend in the castles. When you buy your tickets, your entry time to Hohenschwangau occurs first (because it's closer to the ticket counter), then you have about an hour after the end of your tour at the first castle to walk up hill to Neuschwanstein. You can also visit a museum dedicated to the history of the Bavarian royal family, but you can enter freely at your leisure. No set entry time.
How early to leave Munich depends on a number of factors. If you pre-book your tickets (recommended in the summer, not necessary for most of the rest of the year), you know in advanced how early you need to arrive for your pre-determined entry time. If your visit is not in the summer and you didn't reserve tickets, arriving in Füssen by mid-morning should be early enough. During less busy times of the year, you can arrive rather late in the day and still have a very good chance of seeing both castles.
I have no opinion on whether to stay in Munich or Füssen (or Schwangau). Depends on your preferences and what else you're doing on this trip. Plenty of tourists choose either option and seem happy with each outcome.