Everyone knows the picture: white towers on a limestone crag, forest below, flat land stretching away to the north. What the postcards do not tell you is how many people are in the picture's foreground. The village of Schwangau and the car parks around Hohenschwangau fill with coaches from about ten in the morning, so if you want to see the castle with some room to think, arrive early or come late and treat the visit as a shoulder-season pleasure.
Ludwig II began Neuschwanstein in 1869, as a private fantasy of medieval knighthood and Wagnerian opera, on a hill facing the older castle of Hohenschwangau where he had grown up. He lived in it only for a few months before being declared unfit to rule in 1886 and dying in Lake Starnberg under circumstances that are still argued about. The castle was opened to paying visitors within weeks of his death, which is perhaps the most Bavarian irony available. The view you want is from the Marienbrücke, a steel bridge over the Pöllat gorge, with the waterfall below and the castle across the void. It is a short walk uphill from the village, and in winter the path can be icy.
For riding, the surroundings are better than the sight itself. The land here is where the Alpine foreland meets the first real wall of mountains: the Tegelberg rises behind, the Forggensee reservoir spreads to the north, and the Lech river leaves the mountains at Füssen. Roads over the border to Reutte and the Tyrol begin a few minutes away, and the rolling farm roads toward Roßhaupten and Lechbruck are quiet, curvy and framed by the Alps on one side. In clear autumn light with the cows still out, they are some of the nicest low-speed riding in Bavaria.
Füssen, just under four kilometres away, is a proper town with fuel, cafés and a handsome old centre under the High Castle; it was a hub for lute and violin makers in the late Middle Ages and still has a reputation for instruments. Schwangau itself is small, and prices around the castle car parks reflect captive customers. Eat in Füssen instead.
Motorcycle parking exists near the ticket centre, but the road up to the castle itself is closed to private vehicles. Plan on walking, on shoes with grip, and on some patience with selfie sticks.