My wife and I plan to visit Hohenschwangau and Neuschwanstein Castles from Munich on 15th May. The earliest we can reach Hohenschwangau by train using our Bayern Card is 12.13pm. Assuming our first castle tour would begin at 1.30pm (possibly 2pm), should we restrict ourselves to the Neuschwanstein tour so that we don't get back to Munich too late? How long does it take to visit both castles, taking into account non-tour sightseeing at both places?

First, you can visit the Hohenshwangau website, www.hohenschwangau.de, and reserve tickets for the tours. They must be picked up at least an hour before the tour. Then you have to get up to Neuschwanstein, which should take 15-30 minutes if you walk, but here are horse carriages to take you up and also a bus. The bus drops you off by Marienbruecke (a bridge) which has nice views down on the castle. Whether you take the bus or a horse carriage, you will have to walk up the last bit. The tour will be less than an hour, you will also probably want to look around the gift shop. Then you have to go down to the village and up to Hohenschwnagau Palace, which isn't nearly as high up for that tour, which should also be under an hour. Of course, you will want to take a bus or taxi between the train station in Fuessen and Hohenschwangau, so that's additional time.
Some people who want to have more time in Hohenschwangau leave Munich earlier, purchasing tickets to the first place where the train will be after 9AM in addition to their Bavaria Lander ticket.
To me, the pleasure of Neuschwanstein is viewing it at my leisure from different perspectives, lighting conditions, and seasons. (The interior isn't that great, and it was never finished.) The palace with its setting on the edge of the Alps is stunning, stay in Hohenschwangau if you can with close-up views of the lit-up by night castle from your room, in a place such as the excellent small hotel Villa Jaegerhaus.

HI Michael
My husband and I visited south Germany last year. We drove from Zurich to Munich and decided to visit Neuschwanstein castle. Even though it was the middle of summer, itwas cold and raining! Neuschwanstein castle is in the lovely village of Fussen (which I believe is actually in Austria - right on the boarder). It was recommended to us from a friend.
We were only there for a couple of hours, but it was amazing. It was actually very busy, despite the off weather. We caught the shuttle bus (be prepared to wait) up to the castle from the base village area, where you walk 10 or so minutes up to the castle itself. It is huge - big proportions, but the view of the lakes and the alps from up there is breathtaking.
We didn't actually go inside, as we didn't have enough time, but we would have loved to. So I recommend that you do take the day to actually walk up there and go inside. And actually explore the grounds, the views and the village of Fussen aswell. The Bavarian countryside is so picturesque, it's fantastic!
Afroditi.

Thank you marcopolko and ab8i. As I write I am trying to decide whether to tour both castles or only Neuschwanstein, bearing in mind that we have to travel from Munich. At the moment I am leaning towards touring only Neuschwanstein then spending time looking at Hohenschwangau from the outside and then spending some time in Fussen. Does this seem like a good idea?

Just do the one. In addition to all the waiting mentioned above there is usually a wait from the time you buy your ticket to when your tour starts.
Consider night train and hotel in Fussen and get an early start the next AM.
Or rent a car for the day. Then you can visit the very special Linderhof.
Yeah it is worth it, especially if you take your time.

Thanks to all of you. Since starting this post yesterday I've had a rethink (based on your responses). My current plan is to devote one day to touring Neushwanstein Castle and its surrounds and visiting Fussen (leaving out hoheschwangau) and another day to touring Linderhof and visiting Obergammergau. As we are travelling by public transport this will mean that we are less rushed.
Does this seem a good idea?