When you're pressed for time, a good way to see the highlights of Vienna is through a sightseeing bus tour, which gives you a speedy tour around the heart of the city and allows a closer look at the Schönbrunn and Belvedere palaces. You can cover almost the same territory on your own by taking either streetcar No. 1 or No. 2 around the Ring. (Streetcar No. 1 runs from Staatsoper to Schwedenplatz, and streetcar No. 2 runs from Schwedenplatz to Staatsoper.) For tours, there are a couple of reputable firms: Vienna Sightseeing Tours and Cityrama Sightseeing. Both run daily "get-acquainted" tours lasting about three hours (€39), including visits to the Schönbrunn and Belvedere palace grounds. Both firms provide hotel pickup for most tours.
You can tour at your own pace with Vienna Sightseeing's Hop On, Hop Off bus tour. There are 15 stops, and a day ticket purchased after 3 pm is valid for the whole next day, too. The short city tour costs €13 and does a run around the major sites in about an hour. The day ticket for €20 allows far more freedom. All tickets can be purchased at hotels, at the bus stops, and on the bus. The first bus leaves the Opera stop at 10 am and every half hour after until 6 pm.
A Fiaker, or horse carriage, will trot you around to whatever destination you specify, but this is an expensive way to see the city. A short tour of the inner city takes about 20 minutes and costs €45; a longer one including the inner city and part of the Ringstrasse lasts about 40 minutes and costs €70; and an hour-long tour of the inner city and the whole Ringstrasse costs €95. The carriages accommodate four (five if someone sits next to the coachman). Starting points are Heldenplatz in front of the Hofburg, Stephansplatz beside the cathedral, and across from the Albertina, all in the 1st District.
Guided walking tours are a great way to see the city highlights. The tourist office offers around 40 tour topics, ranging from "Unknown Underground Vienna" to "Hollywood in Vienna" to "Jewish Families and Their Past in Vienna." Vienna Walks and Talks offers informative walks through the old Jewish Quarter and a Third Man tour about the classic film starring Orson Welles. Tours take about 1½ hours, are held in any weather provided at least three people turn up, and cost €14, plus any entry fees. No reservations are needed. Ask for the monthly brochure "Walks in Vienna," which details the tours, days, times, and starting points.
If you can, try to get a copy of Henriette Mandl's "Vienna Downtown Walking Tours" from a bookshop. The six tours take you through the highlights of central Vienna, with excellent commentary and some entertaining anecdotes that most of your Viennese acquaintances won't know.