You're talking about one of my favourite places in the world and I know it really, really well. try
www.wien.at for starters plus the others shown above.
Public transport is excellent in Vienna and the Underground especially is easy to use. Free maps are available in most hotels and help with getting around.
Yes, Schoenbrunn (take the Underground U4 to Schoenbrunn), the Hofburg, the State Opera House are must-sees but so are: St Stepansdom, the Votivkirche, Karlskirche and the Musikverein plus a trip to the Museumsquartier (again on the Underground or just walk there depending on where you're staying), the Kunsthistorischesmuseum, the Mueum der Stadt Wien and MUMOK. A little further and, this time, a trip on a tram (Strassenbahn), to visit the Hundertwasserhaus and Kunsthaus Wien (great for a spot of lunch too) The Herrengeschichtemuseum is fascinating as well.
Chill out in the Stadtpark and try the Third Man tour. For an itneresting shopping experience, get on the Underground again and go to Gasometer. Mariahilferstrasse and Kaerntnerstrasse are also key shopping streets and in the latter you get street performers too (some of them are classically trained!)
Eating is good in Vienna and the Wienerwald chain offer excellent value for money or you can go upmarket and eat at the Grand Hotel or the Restaurant Korso (Hotel Bristol), not to mention the Sacher....
PM me if you want more info! I could go on but I'm getting very nostalgic so I'll stop. It's a fabulous, romantic, cultural, historic and stunning city. Have a wonderful time!
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http://www.catherinecavendish.comIf you think you're too small to be effective, you have never been in bed with a mosquito