The way up to the castle is an easy walk and takes about 35 minutes. You can manage it with whatever shoes you are wearing, but I would recommend you to wear some comfy sneakers. The view of the Neuschwanstein Castle if you follow the official way up to the castle (the entrance part is still under reconstruction).

When visiting Neuschwanstein Castle in Bavaria, you should wear comfortable, high-traction walking shoes and dress in layers, regardless of the season. The castle is located on a steep hill, and the walk from the village of Hohenschwangau to the castle entrance takes about 30–40 minutes uphill on a paved but sometimes slick path. Even if you take the shuttle bus or horse-drawn carriage, there is still significant walking and standing involved, including many stairs inside the castle. Because the castle is in the foothills of the Alps, weather can change rapidly; even on a sunny day, it can be breezy and cool at the Marienbrücke (Mary's Bridge). In summer, breathable fabrics are best, but always carry a light rain jacket. In winter, the path can be icy, so boots with good grip are essential. If you plan to hike the scenic trails surrounding the castle for better photo angles, sturdy hiking shoes or sneakers are a must. Avoid formal or restrictive clothing, as the visit is quite physically active despite the fairy-tale setting.