Below is our interactive Neuschwanstein map showing the castle, our recommended hotel, and the train station in Fussen, the place most folks stay when they visit Neuschwanstein. You can see the beauty of this area, and it's worth a three day stay if you like stunning rural scenery.
Neuschwanstein Travel Toolbox 
Neuschwanstein Castle is the exclamation point along the Romantic Road. Go north and you'll discover towns like Rothenburg and Dinkelsbühl. Afterwards, you can visit Munich or head into Austria--It's just over the border.
Neuschwanstein's foundation stone was set on September 5th, 1869. When King Ludwig II died in 1886, the castle was still not complete. Ludwig's aim was to to replicate medieval architecture, especially the Romanesque, and to pay homage to the operas of Wagner.
Tickets
Entrance tickets to the castle must be purchased at the ticket center in Hohenschwangau before you start the climb to the castle. In 2017, tickets cost 13 euro. Here is information on tickets and opening hours of the castle.
From Neuschwanstein Castle there are great views of alpine lakes, especially the Alpsee, which you can see on the map (and in the picture to the right). Hiking trails abound near the Alpsee, and the one circling the lake is protected as a nature reserve.
Weather and When to Go
Since we're in the Alps, expect snow in the cool period between November and April--but the scenery is beautiful then. Many travelers like the fall. September and October are the driest months, and the daytime temperatures are still warm.
The folks to the right are enjoying the Alpsee at the end of June. The days were glorious, the nights cool.
Getting There and Getting Around
By car: Take the A7 to Füssen, then on to Hohenschwangau where you'll find parking. From Hohenschwangau you can walk to the castle in 30 minutes.
By rail: Take the train to the town of Füssen, then bus 9713 to Hohenschwangau.
Traveling by car between short walks is the usual way folks experience the area.
Staying
We very much enjoyed our stay at Hotel Müller (marked on map). The restaurant was fantastic.
Many folks stay in Fussen. If that is your choice, then here are some convenient Hotels around the Fussen Train Station.