The prior poster seems to want you to experience what he finds vital, despite your wish to see Santorini, adding hundreds of miles of driving, and overlooking the fact that you arrive waay after dark. With only 8 days, please put that agenda aside. Instead let's seek a sensible itinerary, minimizing travel time, maximizing fun time. (BTW, i always wish people gave EXACT dates, you get better advice, why be vague, is arrival June 3 or June 10 ??). Also, no harm saying where you're from (unless u are in Witness Protection program LOL); I'm guessing from late-night arrival that you'll come from Far West, with 2 plane changes, 20+ hour duration & will be exhausted. It affects plans!
He's right about 1 thing; with only 8 days, it wastes precious time to go into Athens TWICE; save it for the end. Instead, get a rental car, check into small place very near Airport, St Thomas B&B http://www.stay-in-athens.com (or if it's full, a more basic place but well-reviewed - http://www.perishotelapt.gr. First action: sleep!!
SUN, Day 2 - drive to Delphi (3.5 hours); bus tour crowds are from 10:30 - 1 pm, so time it to arrive as they leave; can enjoy museum, ancient site, sunset dinner on terrace looking down mountain to sea. From here on, you must choose between 2 options... and either will require domestic flights to achieve -- and please note: book ONLY AEgean or Olympic (same owner; top-rated) NOT Ryan, Sky Express, Volotea; BAD reviews.
• You REALLY need 2 full days/nights in Athens for the remarkable history/landmarks, and it's very enjoyable in June -- so that leaves M-T-W-Th and F for either 1 island or 2... depending on WHAT you want.
(A) You can spend the whole time in Santorini, lolling on a balcony, gazing at the Famous Caldera View & drinking wine ... and it will be (albeit co$$tly) relaxing. But you will not "experience the culture". It's so touricized you'll mostly hear English, be surrounded by huge cruise crowds and package- tour throngs. Even the waiters are Bulgarian.
(B) OR, you could do 48 hours in Santorini then 48-70 hours in nearby NAXOS, to get an experience of a Golden-sand beach (Santorini is either Pool or black-grit beach), a lively island with only independent travelers, dramatic mountain landscapes, and ancient history all around.
ACTION/(A) - • ACTION: Leave Delphi Mon 6:45 AM latest, Arriv Airport 10:15, return car, check in for 10:45 AEGEAN AIR $172 per pers. Arr Santorini 11:45. Leave Santorini FRI (Midday=$150pp; 6-9=$84). OR Ferry (9hrs/$70+).
ACTION (B) Same as (A) arr SANTO Mon 1145. Wed 3:15pm BLUE STAR ferry to NAXOS 2hrs. NAXOS W-Th nites, Fri day, then 6PM BLUE STAR ferry($38pp).. Arr PIRAEUS (Ath) midnight. Metro to ATH hotel.
BTW, there is no time to Dither; flights for June already are selling out. Settle your TRANSPORT first, only afterwards lodging. There's always a "plan B" for hotels, not for planes. I've been to both these islands many many times, and am happy to advise on places to stay once you get an itinerary set.