You may disagree but most of us "old hands" would reverse your sequence. With such a cruelly short visit, not only days, but HOURS become important, and you waste precious hours by going in to central athens twice -- the process takes HOURs by the time yo check in/check out take bus or metro or taxi. Instead, you should fly immediately to your first island and work your way back, and save Athens for the last. Also, in such a brief trip, taking a day ferry to a cyclades island eats up an entire day --you should fly instead. Yes, it costs more, but when you cannot spare the time, you must spare the money.
The critical thing is, you must act SOON -- if you dither too long, the flights are gone. Don't worry about hotels until you've figured out the logistics. One can always find another hotel, but if a fllight is gone, that's that. Now, if you go NOW to http://en.aegeanair.com -- you will see that there's a Santorini flight at 10:15 (too early to make) and 13:10 -- that's 1:10 pm. Arrives 1:55 ... u can be on your balcony by 3! It's only €79 if you are traveling quite light (just hand luggage 17 lbs or less) or €101 per, if you have the customary 15-20" rollaboard. From there the sequence I would suggest:
Day 1 (half day), Day 2, Day 3 morning - Santorini Book a hotel on the Caldera side for the view; the santorini beaches are black/gritty, and on May 6, water's still too cold anyway
Day 3 @ 3:15 PM -- sail on BLUE STAR ferry (open decks, big modern boat, wonderful!!) take pix of Santo as you depart ... arrive NAXOS 5:30. Stay in hotel on St. George (Ag. Giorgios) beach directly adjoining the port town -- most hotels will meet the ferry with car or shuttle, but it's also an easy 15-minute walk.
Day 3 evening, day 4, day 5 -- Enjoy Naxos! Ag. Giorgios is shallow beach but yay! that means it's swimmable by May 10 (Ive done it)... here's a look - http://www.flickr.com/photos/stanbr54/sets/72157632094558042/ also MUCH to do, enjoy all around Naxos http://www.flickr.com/photos/stanbr54/sets/72157634605629689/ including hill villagee https://www.flickr.com/photos/stanbr54/sets/72157632110674306/ Naxos has landscapes, beaches, ruins, history, a STUNNING tiny museum up in the Kastro heights ... you won't even get started on Naxos delights in 2 days -- you may decide to add a day to it
DAy 5 (OR day 6) evening -- take 6 PM BLUE STAR Ferry, get "reserved" ecoomy seats (lean-back, comfy just 4E more than reg economy). Sit out on deck for sunset, snack at a cafe, then snooze in your resrved seat, arrival around midnight. Taxi to an athens hotel doubles at midnight toabout €50+, but find another couple on board to go to ONE destination & you will just be charged the 1 taxi fare, to split.
DAY 6 - 7 - 8 (or just 7 & 8) -- ATHENS sightseeing. I myself wouldn't try to squeeze in Dellphi. But if you insist, then do not take a "tour" because a tour wastes hours picking up/dropping off... only gets to Dellphi by about 11, rushes you thru the ruins in 1+ hour, then 1 hour museum, then drags u for a taverna meal YOU buy, and stop-offs at souvenir shops (kickbacks??). Instead, on Day 8, get up at crack-o-dawn, get to Lission Bus Station for 7:30 KTEL (Intercity) bus -- arrive Delphi 10:30 ... and catch last bus back to Athens 6:30pm. Pack picnic lunch the night before and enjoy it sitting on a column on a high hill... much better than in a taverna w 30+ bus tourists. But As I said, I think another day on Naxos will yield more memories that a loong trip to/from Delphi just because you've heard about it. When you only have 8 days, you can't pour a quart into a pint bottle. You stat that you want a laid-back trip -- the only way to achieve that is to edit your "wish list" realistically.
YOu will notice I omitted Mykonos -- Santorini & Mykonos are the most ballyhooed overtouricized of all the isles -- but at Least Santorini has the Famous View. Mykonos has a lovely port town (but so does Naxos) ... and Mykonos town is overwhelmed almost daily by 6- 8,000 cruise throngs from MegaShips (which Naxos does NOT have).
HOtels & other details come later. That domestic flight cannot wait. PS: No need to buy ferry tix until day it sails. Good luck & good planning -- when you've committed to definite dates (AND that air ticket), will be glad to chip in some hotel suggestions. Good luck and congratulations -- May is the ideal time to see greece for the first time!