Obviously, I am in the minority here, but I am not a big fan of VIE. I am not a big museum fan, and I fit into the "just hang out" type of traveler. But I have not found VIE to be one of my favorites. I think Budapest is terrific, and have been there many, many times. I think the OP will really enjoy having the opportunity to spend time there.

Just a random thought... if I was in this position, I would head east and visit Romania a bit. As a country that is going through some of the more dramatic change in the region these days (as Budapest did years ago), I find it to be an incredibly interesting place. From Budapest, it is a very easy drive to Oradea or Cluj. Brasov is a nice place to spend a day or two.

There are discount airlines all over the place in the region these days... so getting around should not be that big a problem. Personally, I would suggest skipping VIE in favor of a trip in the other direction. (I'll step off my soapbox now.)