Hydra is one that is constantly promoted by the RS tours & books -- mainly because it's easy to fit in as a one-day befoe or after his sponsored Mainland tours, and he has no island tours. Frankly afte seeing Santorini, why make a special trip to Hydra? Why not instead go to one of the islands that are nearest to Santorini, instead of making a special side trip to Hydra? You have NOT said how you are returning from Santorini.
The standard most time-efficient effort-efficient way that we "Greece Old Hands" recommend to combine mainland & Islands is as follows: Land in ATH - and right away (allowing 2 hours in between) board a plane to your most-distant island... in your case, Santorini. Yes I know you'll be tired after that loooong trek from SF but believe me, it's a lot nicer to wake up y our first morning on an island than in a busy national capital! Spend your 3 days or so in Santorini... then take a ferry to the nearest ineresting island, maybe Naxos or Paros. I suggest Naxos mainly because its Port Town is the more ineresting of the 2... and you could stay at a nice beach (Ag Giorgios) directly adjacent to Port town.... a 10-min walk to all the cafes, shops , museums & other Naxos interests. After 3 days perhaps, FLY backto ATH airport. THat's where you pick up your rental car & head for the Peloponnese. Modern intercity highway, multi-lane, no stops until after Corinth Canal, a piece of cake to drive. Spend howver many days (7-8?) then back to airport to turn in car. Taxi to Central Athens hotel for remainder of your stay.