Parking
Neuschwanstein Castle is situated near Schwangau and Füssen in the Allgäu. The pathway to walk to the castle starts in Hohenschwangau (a nearby village). There is parking available in Hohenschwangau but this is about as close as you'll be able to get by car.
Directions
Take the A7 autobahn (direction Ulm-Kempten-Füssen) right to the end and then head in the direction of Füssen. From Füssen follow the B17 to Schwangau, then the signs to Hohenschwangau.
Or
Get off the A7 at the exit for Kempten and follow the B12 to Marktoberdorf. From there follow the B16 to Roßhaupten – OAL I to Buching – and then take the B17 to Schwangau and Hohenschwangau.