Totally loved the The Art History Museum ( Kunsthistoriches ) -- amazing musuem not to be missed and a wonderful cafe in the museum where I went for a very good lunch. I spent most of the day in the museum and did not see it all.
I enjoyed the Belvedere Palace and the palace gardens, again spent most of the day there too! I stayed longer than most people because I enjoyed the gardens and seeing all the grounds and spent time going into each room to see every painting. Had a nice lunch in their cafe at the palace too. Not as amazing as the Kunsthistoriches but good enough. I did not go to the Lower Belvedere as I did not care for the art exhibit they were having at the time. But the Belvedere Palace is lovely, no furniture, just paintings and of course some key works by Kimt including the Kiss.
I spent 4 extra days in Vienna after the GAS tour and did not have the time to go to the Schonbrunn which I was very disppointed about so that is on top of my list should I return to Vienna. I did have friends from the tour and they spent a lot of time seeing the gardens but did not have time to see the inside of the palace. It really is a whole day at the Schonbrunn if you go.
Vienna is a lovely city, easy to get around, very good trams and metro system. Lots of concerts, opera to see and just wonderful museums and cafes.
I agree with you completely, I also feel you should skip the Lourve and see the D'Orsay if you don't have time for both when in Paris!
Have a great time.