TICKETS: Tickets for many of Vienna's musical events can be hard to come by at Christmas time, especially for the Philharmonic and the State Opera's traditional New Year's Eve performance of "Die Fledermaus." Sometimes the major hotels and ticket bureaus can get these tickets -- but at a hefty price.

Tickets for other performances of the State Opera and Volksoper can be ordered through the Austrian Tourist Information Office (500 Fifth Ave., New York, N.Y. 10110, 212-944-6880) or bought at the state theater ticket bureau (Goethegasse 1, 1010 Vienna) or through hotel concierges or ticket bureaus throughout the city. American Express, on Kaerntnerstrasse, often has tickets for the Boys Choir and the Spanish Riding School. MUSEUMS: Many of Vienna's museums mount special exhibits for the holiday season. An "Austrian Christmas" is planned for the Volkshalle in the Rathaus through Dec. 24, and a display of creches in St. Peter's Church through Dec. 13. The Folklore Museum will be showing antique Christmas cribs through Feb. 2. The Kuenstlerhaus opens a six-month exhibition on the "Age of Biedermeier" on Dec. 17; the Museum of the 20th Century will show "Art in Central Europe Since 1960"; and the Museum of the City of Vienna will have an exhibition entitled "Vienna's Jewish Community: Items From the Collection of Max Berger" from Dec. 11 through Feb. 21. The Clock Museum and the Hofburg's Collection of Old Musical Instruments both offer themes in time (or in tune) with the season. SIDE TRIPS: If you're in Vienna for a few days, you may want to take a side trip.

Close by, in the hills surrounding the flat Danube Valley capital, are the Vienna Woods, especially enchanting after a fresh snowfall but delightful any time; Heiligenkreuz Monastery, a tastefully ornate mixture of Gothic and Romanesque that can be an antidote to the overdose of baroque architecture in the city; and Kahlenberg, the promontory that overlooks Vienna and the Danube from the north. All can be reached by sightseeing buses that leave from in front of the State Opera.

Baden, a popular old resort town 15 miles south of Vienna, can be reached by frequent trolleys that leave from the Ringstrasse near the State Opera.

Other rewarding sites, reachable by bus or train as well as auto, include Eisenstadt, home and burial place of Haydn, with the nicely kept Eszterhazy Palace; Melk, home of an imposing baroque abbey that sits on a hill overlooking the Danube, about 30 miles west of Vienna; and Mariazell, in the foothills of the Alps, southwest of the city, a pilgrimage site since the 12th century and still popular with Europe's Roman Catholics.