First, take advantage of Vienna's public transportation network to get the most out of your time. It's inexpensive, clean, and efficient. A 24 hour network card costs only 6.70 Euro and is valid on U-Bahn trains, buses, street trams, and S-Bahn trains within the city limits. Taking a street tram, Straßenbahn, is a great way to get around with views of the city. With a day card you can hop on and off easily to catch any sight.
Ideally, spend the night before taking your day in the city so you can enjoy a leisurely breakfast Viennese-style. Vienna is famous for its coffee house culture, so no visitor should let this institution go un-sampled, even if you're not a coffee drinker - all coffee houses have wide selections of teas and alcohol to please any palate as well. There are a myriad of venues to sample Vienna's renowned coffee creations, which include the popular Wiener Melange - a mix of equal parts coffee, steamed milk, and foam. A good choice are cafes from the Querfeld Family chain, which offer an old world atmosphere and decor plus quality Viennese or Austrian coffee and food selections in a classic style.
These include Cafe Restaurant Landtmann on Universitätsring (Strassenbahn 1 or D to Rathausplatz/Burgtheater), Cafe Museum at Operngasse 7 (U1, U4, Strassenbahn 1 or 62 to Karlsplatz), Cafe Hofburg on the grounds of the Hofburg Palace, a good breakfast choice if you're going to spend some time touring the former Habsburg residence and its several in-house museums (Innerer Burghof, Hofburg, bus 2A or 3A to Habsburgergasse or U3 to Herrengasse) or Cafe Mozart, often recognized from its role as a meeting spot in the famous film noir set in postwar Vienna, The Third Man (bus 3A to Albertinaplatz).
All of these are located within a short distance in the city center, making them easily visitable on a 24 hour trip and allowing for quick transition to nearby attractions. All are within walking distance to Stephansplatz, the square perhaps best identified as the heart of downtown Vienna, with the famed Gothic St. Stephen's Cathedral (Stephansdom in German). The cathedral is a landmark of the city, and a visit offers stunning views of the architecture and interior, plus a unique tour through the underground crypts for some history. From the cathedral, a walk through Stephansplatz and the surrounding small streets of the city centre is essential. Vienna's centre is compact, easily walkable, and offers many opportunities for local food, drink, souvenir shopping, museums, historical churches, squares, and other sights. Taking an hour or two for a walk here is the best way to soak up the history and lively culture of the city.
Vienna's landscape is scattered with former imperial palaces, giving the city its distinct connection to this rich past and offering some of the best options for visitors to experience some of its interesting history. Art lovers should seek out the Belvedere, a Baroque palace complex with Orangery, park and gardens, and stables, now the setting for a collection of Austrian art, including works from the Fin de Siecle era, the Viennese Secession with pieces from Gustav Klimt and Egon Schiele, and a section of interest for children. Take Strassenbahn D to Schloss Belvedere or numbers 18 or 0 to Südbahnhof, or the U1 to Südtirolerplatz.
If a broader scope of the city's culture sounds appealing, stroll through the Hofburg, the main palace conveniently found in Vienna's centre and reachable on a walk from Stephansplatz. Located within this Habsburg palace are a number of museums including the Imperial Apartments and Treasury, Silver Collection, and Sisi Museum dedicated to the Habsburg Empress who so intensely captivated the hearts and imaginations of the Empire, and the National Library, among other culturally valuable institutions.
Outside of the Hofburg is the beautiful Volksgarten, a park with great expanses of greenery and relaxed atmosphere. It makes for an idyllic spot to stroll after a morning of museum-going or to pause for picnic lunch in warm weather. Just across the Burgring from the main Hofburg collections is the Kunsthistorisches (Art History) Museum, and on the nearby Museumsplatz is the MuseumsQuartier, a modern and sleekly designed complex of several excellent museums including the Leopold (modern Austrian art), Kunsthalle Wien, Museum of Modern Art, the Architektur Zentrum, and Zoom Kindermuseum. MuseumsQuartier is bordered by Maria-Theresien-Platz, a square and park which in summer are lovely spots for walking or relaxing and taking a rest during a day of sightseeing.
From mid-November through the end of the year it's the site of a traditional Christmas market, with stalls of Austrian holiday food specialties, spiced wines and cocoas, and crafts. In winter a visit to the Christmas market is a delightful and traditional way to spend your time in Vienna and enjoy the festive atmosphere.
For a change of the scenery from the centre, hop on the U4 metro line, direction Hütteldorf, to Schönbrunn - the famed and beautiful summer residence palace of the Habsburgs. Schönbrunn palace is a must-see as it embodies all of the splendour and majesty of Imperial Vienna in a stunning landscape. Tours through the palace are available if regal interiors, royal family memorabilia, and high imperial wealth are of interest, but Schönbrunn is worth a visit even if you don't go inside.
Behind the palace lies a magnificent layout of meticulously landscaped park and gardens, studded with an array of beautiful fountains and sculptures, a labyrinth, restaurants and cafes, a zoo, and the architecturally Gloriette on a hill overlooking the center gardens. The picturesque landscape makes the perfect spot for a picnic in warm weather, but is beautiful for a walk and worth seeing in any weather.
To finish your day, head back to the centre for dinner. The same coffee houses with Viennese breakfast services offer a variety of traditional Austrian dishes, usually meat-based, for dinner. Try the legendary Cafe Central or Cafe Griensteidl at Michaelerplatz, both former haunts of many famous intellectuals and artists throughout the years. Vienna's most iconic dish is the Wiener Schnitzel, an extremely thin cut of veal breaded and fried and served with lemon and a special, vinegary Austrian potato salad.
Vienna's best sample of the dish is allegedly found at the restaurant Figlmüller at Wollzeile 5, just off of Stephansplatz. Try it here or anywhere it's served, for such an important dish it's made with care at restaurants throughout the city. Follow it up with a slice of Sachertorte for dessert, Vienna's most famous pastry said to have originated in the Hotel Sacher and made of chocolate, apricot jam, and chocolate glaze. End your evening with a glass of schnapps or another helping of Viennese coffee.