I did the trip the other way round, from Vienna to Budapest. It was a smooth safe ride but I had read dire warnings on the net of pickpockets and fake officials demanding wallets, passports etc - this didn't happen on my trip. The station is quite to the west of Vienna centre but the trams are fantastic. I would get a day ticket then travel into the heart - look round the old streets and cathedral in the city centre - the modern art gallery is fantastic, didn't go in the national museum as I was too hot and it seemed too much of a commitment at my time of life. Ditto Schoenbrunn palace - just too too much in a day. I did go out to the Belvedere and saw all the gorgeous Gustav Klimt paintings but I think they're all at the Liverpool Tate just now. Have a ride on the big wheel in the Prater Park, have some lunch and a few biers and then it'll be time for back to Budapest.