Yes, by all means, take the Strassenbahn out to Grinzing; visit Mahler's grave; take a stroll pass the outdoor wine tables (Heurigen), and continue on into the Wienerwald (not to be confused with the chain of chicken restaurants by the same name). Thoughts of Beethoven, Schubert, Bruckner, Mahler, and all of the other boys, will come to you out there. If you're with a beautiful girl, thoughts of the adult versions of the "Heidi" movies might suddenly come to you
. Anyway, I believe that you can continue all the way to the big cathedral and monastery at Melk, but that would be quite a hike. It's a beautiful Rococo style cathedral - well worth seeing.
Back in town, I would say to avoid many of the usual claptraps - especially in summer - and take a taxi or bus to see the outrageous
Kirche am Steinhof, designed by the amazing Otto Wagner. For some reason, they keep this church off the usual Vienna tours. Regardless, I think it's my favorite church on the entire planet!
As a primer on what Vienna was like after WWII - and when the city was still occupied by the four victorious allied nations (the famous, "four in a jeep" period) - I would urge you to take a look at Carol Reed's "The Third Man", staring Orson Welles and Joseph Cotton.
By "usual claptraps", I would include The Hofburg; St. Stephensdom (cathedral); the Staatsoper (unless a good production of a good opera happens to be on); any "blue" Danube tours; and most certainly Schoenbrunn. I would, however, take a look at the Klimt paintings at the Lower Belvedere - assuming that there still are some Klimt paintings there. Regardless, both the upper and lower Belvedere are far more interesting to look at than Schoenbrunn (a tacky, mini Versailles - equally excessive).
I haven't been to Wien since 1980, and the Secession building was closed to the public. It's been fixed up and reopened to the public since then. However, I don't think that the Beethoven Frieze - the one that shows Mahler as a Teutonic knight - is on permanent display there. Maybe it is. Anyway, go see it!
In general, I would avoid most everything that is baroque period, and chase after architecture and art that was affiliated with the Austrian brand of Art Nouveau, known locally as
Jugendstil. That was the period of Mahler, Klimt, Otto Wagner, Alfred Loos, and many other turn-of-the-century Viennese artists, architects, writers, playwrights (Arthus Schnitzler), etc. If any tour has Johann Strauss music accompanying it, avoid it!!!
I'll finish by saying that deep in my middle age, Vienna and Los Angeles (sans smog) are my two most favorites cities on the entire planet - what little of it I know it, that is. To me, it's no mystery that so many of the Jewish emigres from the Hitler period settled in L.A.
