Absolutely get busy with bookings!! Your best experience will depend VERY much on location, location, location ... and since you'll need 2 rooms, and when you wait until arrival, you may be stuck with a place that's inconvenient, far from a bus line, no views. In late May, if you spend some time & do online homework, you can find good places at good prices. Some Ideas on the modest-budget level --
• FIRST NIGHT -- Look at budget Hotel Peris, Hotel Pantheon; about a 10-15 taxi ride away. You won't get there til 10pm and probably will be checking out at 6 am or earlier, so your needs are just comfy beds, good A/c, and these 2 will deliver. But do book.
• SANTORINI -- Consider staying in FIROSTEPHANI, at north edge of FIRA, a "goldilocks choice" -- away from daytime tourist superthrongs of OIA and FIRA, yet also on or near the famous rimside view, and easy 15-minute walk to/from Fira cafes, museums etc. Book NOW - because honeymooners already snapping up best bargains.
• NAXOS - Teens always want independence, being able to wander safely, not be stuck with parents only in isolated spots - so for you, Accoms on St. George (Ag Giorgios) beach directly adjacent to Naxos Town, is ideal. Not overcrowded in late may but lots of other teens on beach, at Watersports center... and it's a 15-minute stroll to Port town. NOTE: many beach-side lodgings offer 1-BR "self-catering" -- a BR, plus main room w. 2 day-beds, kitchenette, balcony. If these all books, then u can often get 2 "studio" units side by side.
• ISLAND TIME - I'd subtract 1 night from Santorini, (you still have 48 hours - arriving 9 am, and leaving AM day 3) - 2 days enuf to see Famous View, check arch. dig -- beaches are not much to visit). Add the day to Naxos.
• ATHENS #1 OPTION - I agree, day trips unsatisfactory, too rushed. As Suki devote 3 days to Athens, then check out and go to Wonderful Nafplio & Argolid... a super teen adventure. here's a Noncommercial website: http://www.visitnafplio.com/ plus a photo album with some highlights: http://www.flickr.com/photos/stanbr54/sets/72157632094108982/ Check ALL website links. Some TeenWorthy doings - NEMEA, just off main highway, a "runner-up" to Olympia as Games Site -- PALAMIDI, amazing high fortress above Napflio Old town, 999 steps up (but u can drive up b ackway and have kids walk Down), ACRONAFPLIA and BOURTZOI, 2 more castles to conquer! ARCH. MUSEUM (an Achilles-era suit of armor!), Last Beach Day! -- either the fun Town Beach, or nearby Sandy TOLO ... On Drive back to Athens. EPIDAURUS Theatre (Amazing; 15,000 seats, perfect acoustics), then drive up coast road, jump off at ISTHMUS exit to see/photo Old Bridge over Corinth Canal. Final night near Airport.
• ATHENS #2 OPTION -- Same adventure list -- Only difference: on arrival on Mainland, do Argolid trip FIRST. Either at Airport or at Piraeus, u can pick up rental Car, avoid city traffic get on the MOdern divided intercity highway, no stops until after Corinth Canal. This map - http://euro-map.com/karty-grecii/peloponnes/podrobnaya-turisticheskaya-karta-peloponnesa.jpg - shows entire route plus all the sits mentioned above. NOTE: many agencies allow car pick-up at one Athens site, drop-off at another at no extra €