Itinerary Question

Too much travel for only 8 days (first day doesn't count). You arrive late afternoon ATH airport. why go into town check into hotel (doing all that will take 2 hours), then ditto in early AM. Why not just stay in Airport and get first convenient flight after arrival (allow 2 hrs layover) to Santorini. You fail to tell us WHEN this trip is scheduled -- but there are numerous flight to Santorini ... and by acting now to sign up for Aegean air newlstter (really an e-mail alert system) you might be able to score a discount ticket. Anyway, you could be in Santorini in time for a lae dinner... and wake up to a fab View! With this approach I would suggest:
Day + night, for Day 2 & 3 - Santorini
Earliest AM -- Day 4: fly back to ATH airport, u would be there by 8, get car & drive to Nafplio on the modern intercity hiway... 2.5 hours if you go straight, an hour or so more if you take a couple of quickie turnoffs (1) at Isthmia, just to see the tiny (deep!) Corinth Canal from original bridge, then right back on hiway and then (2) 15 miles or so over canal, jump off and go 4-5miles to Ancient NEMEA -- the runner Sacred-Games site to Olympia. Temple, columns, amazing stadium, and NO tour crowds... a 1-hr fab experience. To NAFPLIO by noon; spend rest of day exploring old town .. Do NOT overlook GOOD arch. Museum on square (it has world's ONLY set of Iliad-era warrior armor***)
Day 5 - 6 - 7 SO much to see! Mycenae, Asine (+ Tolo Beach), Epidaurus (you can catch this one on your way BACk to Athens by driving E, then taking coast road up to Corinth Canal/Isthmus. And don't neglect enjoying the stunning Nafplio sunsets from long row of seafront cafes (with upholstered loveseat views for the price of a coffee!) .. this is my favorite Greece sunset venue, and you'll be able to compare it with Santorini.
NOTE: I would skip Hydra for lack of time, & after Santorini it would be a let-down anyway.
DAY 8-9 Athens -- Depending on what MONTH u go, best idea for serene Acropolis-exploring is to get there at 8 am, then u have 90 minutes before tour crowds throng in ... then u go down to Agora area if u want ... New Acropolis Museum has a lovely terrace (glassed in & A/C for hot months) lookin up at Parthenon. AND prices v. moderate!

Agree that if possible you should fly to Santorini for night 1. You could spend 3 nights/2 days in Santorini and add one night to Nafplio. Also agree Corinth Canal and Nemea are worthwhile stops. In Nafplio Palamidi Fort is interesting. Mycenae and Epidaurus are also must see. Spending nights 8-9 in Athens will give you 1.5 days or less but with good planning it should be enough time.

You need to research the sights you're interested in and then decide how much time to spend in each town.

Thanks for the advice. I haven't booked anything yet. Wasn't planning on going into Athens on the first night, but was going to stay near the airport, I've found several small hotels with great reviews near the airport with free pickup/dropoff. Flying out to Santorini the night of arrival makes sense, but I get nervous if the connecting flight in Europe runs late. But that is a good idea.

Getting a flight out on arrival day is a good idea. It works well if
(1) you allow a 2-hour layover time between your scheduled arrival and the Santorini plane departure (i.e., arrival 5, 7 pm Santorini departure), which gives time for getting thru Passport Control, claiming bags, hitting the ATM, and checking in to Domestic air .. they require 45-60 minutes before their departure

(2) and IF there is no undue delay resulting from a connection in Europe, OR a huge arrival day in ATH. That, in turn, depends on when you are coming. From now thru July 1, little problem. July-August, high season, MUCH traffic from Europe to Greece. In that case, I'd look for a 3-hour layover, just in case of that connection jam-up.

Hydra is pretty easy to cut, since you will already have a great island under your belt, and the Peloponnese has lots to see with your rental car and without adding a ferry to the mix.