Fritlz is too kind...I've been to Greece three times in the past 12 years, but my last visit was in 2009 and can give some opinions.
Let's say you depart the US on a Saturday, arrive in Athens Sunday.
01 Sun Athens - 1/2 day with jet-lag and hotel checkin
02 Mon Athens
03 Tue Athens
04 Wed Athens-Santorini travel
05 Thu Santorini
06 Fri Santorini
07 Sat Santorini-?? travel
08 Sun ??
09 Mon ??-Athens
10 Tue Depart Athens
Between the Acropolis and its new museum, the other museums in the area and just exploring central Athens, you can fill two days easily. If you do arrive on a Sunday, lots of things may be closed. It'd probably be better to depart the US on a Tues or Wed so that you can have Wed-Fri or Thr-Sat in Athens, then go to Santorini.
Santorini is not to be missed for sure, but I think 4 nights is too much. You can take the high-speed (hyrdofoil) ferry from Athens to Santorini. It's fun to do once, especially coming in and circling the caldera. Then a harrowing taxi ride up the cliffside to the town. That's how I did it in 2005: arrive by ferry and depart by plane. While there, do take the bus up to Oia, a town on the tip of the island crescent, and stay for the sunset.
Getting from Santorini to another island can be a hassle, you pretty much have to go back to Athens first. Back in 2005 I wanted to go from Santorini to Rhodes and the only way was first back to Athens. It may have changed since then, but do check into it when planning. And if most of Greece is on holiday in August, the ferry schedule could be reduced.
I did go to Hydra back in 1999 and I don't have any particularly strong memory one way or another, it kinda blends together with the other 4 islands I visited on that trip. It was nice and all, but I don't know if it was memorable enough to recommend it. If you're intrigued by it, I'm sure you'll enjoy it.
As for Crete, I visited there in 2009 and had an ok time. Knossos is is interesting, but a lot of it is a "restoration" based on the imagination/speculation of Arthur Evans. I guess I had something more academically rigorous in mind. The main city of Crete, Heraklion, is a dump, I don't recommend staying there. I did a day trip to Rethymno, which was much nicer. Crete is such a big island, you really need a car to enjoy it I think. I didn't and the bus system wasn't adequate. So, maybe my experience is unfairly colored by that.
Greece is fantastic, and an easy place to enjoy. I'm sure that with Athens and Santorini you'll have very enjoyable time and whichever you pick for your third stop will be just as good. IMO, since it's a relaxing vacation, take your time and don't try to jam in too many stops. And it might take longer than you think to get from island to island, depending on ferry schedules or flights.
