Maybe not what you had in mind, but I always stay at the Vienna Marriott. Fantastic hotel in a great location. Right on the Ringstrasse, and across the street from Stadtpark. You can easily walk to most things, but there's also a tram stop right outside the hotel, and a couple U-bahn stations within a couple blocks. It can be expensive though, and it's a little more modern if that's not your thing.

Generally speaking, if you haven't been there before, everywhere within the ring is pretty walkable. Any nice hotel will put you in a great location. I'd suggest staying on the southern or eastern quadrants of the ring, if looking at the map. It puts you closest to all the big tourist sites.