THE KING'S CASTLES: Neuschwanstein, Hohenschwangau near Fu ssen, open daily from 8:30 a.m. to 5:30 p.m., admission six marks ($2.72). The castle can be viewed only on guided tours that take approximately 35 minutes and require climbing up 165 steps and climbing down 181. It is a 30- to 45-minute walk up to the castle from the parking lots. Carriage rides up and down take 10 to 15 minutes and cost five marks ($2.27) uphill, three marks ($1.36) downhill.

Hohenschwangau, Hohenschwangau near Fu ssen, open daily from 8:30 a.m. to 5:30 p.m., admission six marks ($2.72). The castle can be viewed only as part of guided tours that take about 35 minutes and require climbing 90 steps.

Linderhof, near Oberammergau, open daily from 9 a.m. to 12:15 p.m. and 12:45 p.m. to 5:30 p.m., admission six marks ($2.72), which includes the Venus Grotto and the Moorish Pavilion.

Schachen Hunting Lodge, on 6,000-foot Mount Schachen, above Partenkirchen, about a two- to three-hour uphill hike, open daily from 8 a.m. to 1 p.m. and 2 p.m. to 6 p.m., though opening times may vary depending on weather; admission two marks (90 cents).

Herrenchiemsee, on Herreninsel, Chiemsee, near Prien, open daily from 9 a.m. to 5 p.m., admission five marks ($2.27). Accessible only by boat from the landing at Prien, round trip 10 marks ($4.54).

PACKAGE TRIPS: Two related tours:

The Seven Day "Royal Tour" (Munich, Garmisch-Partenkirchen, Oberammergau, Starnberg Lake, Prien on the Chiemsee) costs 475 to 593 marks ($215.90 to $269.55) per person, including accommodations, bed-and-breakfast, all entrance fees but not transportation. For booking details: German National Tourist Office, 747 Third Ave., New York, N.Y. 10017, (212) 308-3300.

"Five Days in the Steps of King Ludwig II," including a night in the Schachen Hunting Lodge, costs from 149 marks ($67.72) per person up, depending on accommodations and arrangements. For booking details: Verkehrsamt (Tourist Office), Postfach 1562, D-8100 Garmisch-Partenkirchen, West Germany, phone (49-8821) 53093.

WHERE TO STAY: There are numerous hotels in the areas near the castles, with rates ranging from $40 to $80 double. Among them: Starnberg: Hotel Seehof, 4 Bahnhofsplatz, 8130 Starnberg, phone (08151) 6001. (Delete the first 0 from the phone number if calling from outside West Germany.)

*Berg: Dorint-Seehotel Leoni, 44 Assenbucher Strasse, 8137 Berg-Leoni, (08151) 5911. Strandhotel Schloss Berg, 17 See Strasse, 8137 Berg, (08151) 50021.

Fu ssen: Sailer's Kur-Hotel, 14 Bildhauer-Strum Strasse, 8958 Fu ssen, (08362) 7089).

Schwangau/Hohenschwangau: Hotel Ko nig Ludwig, 11 Kreuzweg, 8959 Schwangau, (08362) 81081. Hotel Lisl-Ja gerhaus, 1 Neuschwansteiner Strasse, 8959 Schwangau-Hohenschwangau, (08362) 81006. Hotel Mu ller, 14 Alpsee Strasse, 8959 Schwangau-Hohenschwangau, (08362) 81056.

Oberammergau: Parkhotel Sonnenhof, 12 Ko nig Ludwig Strasse, 8103 Oberammergau, phone (08822) 971. Hotel Wittelsbach, 21 Dorf Strasse, 8103 Oberammergau, (08822) 4545.

Garmisch-Partenkirchen: Grand Hotel Sonnenbichl, 97 Burg Strasse, 8100 Garmisch-Partenkirchen, (08821) 7020. Clausings Posthotel, 12 Marienplatz, 8100 Garmisch-Partenkirchen, (08821) 58071. Hotel Aschenbrenner, 46 Loisach Strasse, 8100 Garmisch-Partenkirchen, (08821) 58029. Posthotel Partenkirchen, 49 Ludwig Strasse, 8100 Garmisch-Partenkirchen, (08821) 51067. Hotel Boddenberg, 21 Wildenauer Strasse, 8100 Garmisch-Partenkirchen, (08821) 51089.

Prien/Chiemsee: Yachthotel Chiemsee, 49 Harrasser Strasse, 8210 Prien, (08051) 6960. Hotel Bayerischer Hof, 3 Bernauer Strasse, 8210 Prien, (08051) 1095.