Go to a Heuriger. It is a tavern where local winemakers serve their own wine. Examples: Müllers Heuriger & Weingut, Schreiberhaus, Weinbau Zawodsky, but there are many more. Actually, the Gala Dinner will be in one.
Cocktails and Drinks at the 18th floor of Sofitel hotel. A bit expensive but good cocktails and a nice view over Vienna.
Museumsquartier, short MQ. There, you can find a lot of of museums as well as restaurants and bars.
Bar at the 8th floor of the 25 Hour Hotel. There you have a nice view and good music.
Drink in an old traditional coffee house: Café Landtmann, Café Hawelka, Café Sperl, Café Central, Demel K. & K. Hofzuckerbäcker.
Sightseeing
Go along the Ringstraße. It is nice during the day, and even nicer in the evening when the lights are turned on. Along the street, you will see: The University of Vienna, the Parliament as well as Burgtheater (= theater), Hofburg (the president's residence), Rathaus (city hall), Volksgarten, Staatsoper, and much more.
Taking the paternoster. It is an old elevator that does not stop but runs in a circle. It is located in the Rathaus. You must enter the entrance to stair 6 at the north side, which means from the street Felderstraße. Opening hours Mo-Fr 6:30-16:00.
Walk through the city center (old town): Anker Uhr (Stunning clock, Stephansdom, Nationalbibliothek, Albertina Museum, Judenplatz (there is also a Holocaust Memorial), Mozerthaus, Michaelaplatz, Spanische Hofreitschule, ...)
Riesenrad (= Ferris wheel): one of the landmarks of Vienna, located in the Wiener Prater, close to the metro station U1/U2 Praterstern.
Kahlenberg: You can drink a coffee and have a nice view over Vienna. You could combine it with one of the "Heurigen" (A), which are more or less close.
Schönbrunn: Big Park, Palace, Zoo (oldest zoo in the world), Irrgarten (= Labyrinth) and the Gloriette. Have a walk through the park up to the Gloriette and drink a coffee there. If you want to go into the zoo, the labyrinth, or the palace, you have to pay for the entrance. However, it is worthy.
Burggarten (= imperial garden): nice garden, and there is also the Schmetterlingshaus (= butterfly house, with a lot of butterflies inside) and the Palmenhaus (palm house, with palms inside).
Karlskirche: a beautiful church in walking distance of the venue.
Museum der Illusionen: a museum with funny optical illusions.
St. Michael's Church: one of the oldest churches in Vienna.
Votivkirche: a very beautiful church.
Museumsquartier, short MQ. There, you can find a lot of museums as well as restaurants and bars.
Hundertwasserhaus, a house designed by "Hundertwasser", a man who didn't like straight lines. Even the ground in front of the house is not straight.
Haus des Meeres (= Aqua Terra Zoo) is located in an old flak tower from the second world war. There are still four flak towers in Vienna. They are not very beautiful but interesting.
Nationalbibliothek: national library.
Leopold Museum: paintings of Klimt & Schiele
MAK - Österreichisches Museum für angewandte Kunst: museum of applied arts.
Kirche am Steinhof: A church located on the top of a hill where a mental / psychiatric hospital is located.
Kapuzinergruft: kapuziner crypt.
Musikverein: concert hall.
Staatsoper: the opera house of Vienna.
Shopping, Fun, and Relaxing Places
Wiener Prater: Amusement park, roller coaster, Ferris wheel, and much more.
Donauinsel: "The danube island."
Stadtpark: City park.
Burggarten: Imperial garden.
Flea market at Kettenbrückengasse: Every Saturday from 6:30-18:00, close to the metro station U4 "Kettenbrückengasse".