Where to begin...
We want to budget between $4k - $5k, if possible.
Since we'll lose probably about a day's worth, coming from US, I thought about stopping first in Venice, Italy for about 4-5days (if that's a reasonable stay or is 2-3 days is enough in Venice and visit another city nearby for 2day, like Florence?), then fly over to Santorini for about 5-6days, and end our stay in Athens for 3 days, and head home.
I've been doing a little research on Tripadvisor on what places we would like to see, like...
Florence and/or Tuscany- haven't researched much yet
Santorini - hike from Fira to Oia, check out Akrotiri, Red Beach, Wine Tour, etc.
And Athens - Acropolis, Parthenon, Temple Olympian Zeus, Acropolis Museum, Plaka, etc.
Could anyone recommend places in each or one of the cities I've suggested on where to stay that is affordable and not somewhere sketchy? Places to eat? Bars? What's the best way to get around, by ferries, trains, buses?; of course this depends on the city/country we're in.