It's very cultural orientated for tourists around here...so lot's of museums and art stuff to see if you want. Usually always something interesting around!
Must see places....hard to tell for me, I don't think we really have anything monumental crazy epic stuff going like other cities.
The usuals are pretty nice though...Stephansdom, Schönbrunn, Belvedere, The Zoo at Schönbrunn etc if you're into historic background.
It's a nice city overall with lots of bits and pieces here and there, but we don't really have an eiffeltower or something like that....
Eat and drink wise it depends on if you want to party or just have a nice dinner...but both can have around the Schwedenplatz pretty easily.
There are some really nice restaurants around there as well (some a bit hidden tho) that make awesome barbeque style food (or lots of other meat heavy "austrian" style kitchen), with lots of different beers and wine to have alongside (I like Bieradies and Hinterholz for example, awesome ribs)
Lots and lots of "normal" bars too there.
I don't really know how it looks with reservations, so it might be hard to get a spot, but having dinner in the Donauturm is pretty cool. It's kinda like the seattle space neelde I think, turning restaurant at the top.
You can always just take a trip by foot through the inner city, it's not big and you can see lots of stuff going round the Ring or streight somewhere through Erster Bezirk (Innere Stadt).
Prater isn't open that time of the year...at least I think so.
Nature wise there's also a lot of green going on to take a walk.
We had a really awesome beautiful fall, but already now it's not yellow and red anymore, so it will be winter already when you'll be here.
Oh and yeah, obviously you can go take a coffee and sweets anywhere.