Vienna-Salzburg-Prague-Budapest
 

We're planning a 10-day trip to Vienna in early Oct. and want to add some other cities to our travels. Thinking that we need at least 4 full days in Vienna, how should we divide the rest of our time between Salzburg, Prague, and Budapest? If we were to add only two cities, which should we drop? We enjoy historical sites, architecture, art museums, music, local cuisine, and will be able to fly in and/or out of Vienna, Prague, or Budapest.

I would probably skip Salzburg and do Prague-Vienna-Budapest in that order or vice-versa to avoid backtracking. I would stay 4 nights in the first destination (just because the arrival day can be iffy due to jet lag, possible delayed flights, and just general disorientation).

We spent 2 1/2 weeks last July in Budapest (7 days), vienna (4 days) and Prague (4 days). With traveling time (3 plane stops for us from US), and train time, we had 15 full days. This was pretty exhausting, as we don't care for the traveling time and changing hotels/apartments can be tiresome as well. We are not "if it's Tuesday, this must be Belgium" kind of people. I would cut out Salzburg.

We started in Budapest, trained to Vienna, and did a car/hire with Cesky Krumlov in between vienna-Prague.

Particularly in light of your interests, I think it might make most sense to consider trimming your itinerary, not adding to it! For the art and architecture of Vienna alone, 4 full days is a bare minimum IMHO. If you really want, you could probably cram in Salzburg and either Prague or Budapest. Given your interests, I would think you would find it unsatisfying to try to fit Prague AND Budapest AND Vienna into the same 10 day trip.

BTW, do your 10 days include your flights? Time to recover from jet lag? If not, you might want to cut even further!

The good news is that you'll see some wonderful things no matter what you choose.