Vienna's old fortifications were razed in the 19th century, and a ring road around the city center was built instead. So, Vienna being a prime tram city, has two tram lines, numbers 1 and 2, which go around the ring clockwise and counterclockwise (don't know which is which though). In terms of hopping on and off, this is your best option, as the route takes you to all the great sights, ie, the Opera, the Parlament, the big museums, the Hofburg, the "Votivkirche", and a bunch of other things.

Also, don't miss a "Heuriger" restaurant/pub in the Grinzing district - lots of fun (although many many in Grinzing will be touristy). You can get to Grinzing on the tram as well.