Bare minimums from my point of view and my interests:
Rome, 3 full days
Florence, 1 full day
Salzburg, naaaa, I wouldn’t give up any time in another location to spend time in Salzburg. Maybe an overnight.
Vienna, 2 full days
Istanbul, 2 full days
Remember I said absolute minimums for my taste. It will provide a good sampling then you can go back some day if something lights your fire. BUT, Italy combined with Central Europe is sort of a stretch and for the type of value I try and get out of a trip it puts too much time in travel vs seeing what I go to Europe to see. I try and tie things together geographically and thematically (is that a word?). I would do (and sort of have done)
Flight to Sofia 2 nights
Car to Plovdiv 2 nights
Car to Veliko Tarnavo 1 night
Car to Varna 2 nights
Car to Istanbul 3 nights
Flight to Budapest 4 nights
Train to Vienna 3 nights
Too long a trip? You could get by with one night in Sofia if you leave late the next day to Plovdiv and you could get by with 2 nights in Vienna if you leave Budapest on an early morning train. So that’s 15 days minimum and two weeks is 16 days (counting the extra weekend). For Salzburg, you could do an overnight trip out of Vienna and then back to Vienna for another day.
And Italy? You can spend two weeks in Italy alone and never scratch the surface.