In early May you'll probably have a better time on the super-popular islands than if you were going in High season. Santorini, Mykonos, Ios, Rhodes, and Samos are all pretty packed and touristy in high season. Obviously they're popular for a reason, though!
Where you should go depends on what you want out of Greece. If you want sight-seeing and a good time, hit up those places for sure and don't ignore Athens. If you want some more off-the-beaten-path type experiences there are lots to be had but you need to work a little harder (and be REALLY sure you know when the ferries are running in the low season). It's really easy to roll into Athens and grab an island tour for however long you want and it'll hit the hot spots. If you want weirder experiences like being "stranded" due to choppy seas on a fishing island of 800 people -- in the middle of their annual fishing festival! -- you need to travel more extemporaneously.
Patmos was my favorite place ... it was gorgeous, not very busy, not really expensive, and still had some remarkable old stuff to check out. If you're planning to spend a couple days in one place, rent a car. It's really, really worth the money to be that mobile. I rented one on Patmos and saw almost every single corner of the island in two days. I saw some incredible things I would have missed if I had limited myself to bumming around Skala (the harbor) and Hora (where St. John's monastery is).
My biggest recommendation: don't order anything by looking at the menu. Ask what the chef thinks you should eat. And if he or she's not busy chat him up! Greeks are pretty entertaining even if you don't really understand what they're going on about because your Greek sucks and so does their English.
You'll find them pretty hospitable in May though .. they get a bit more jaded and worn-out toward the end of tourist season.
Ferries: I'll say again what @theCBE said. Avoid travel bureaus if you can. Also the high-speed Hydrofoils are pretty sweet. They ain't cheap but they'll cut the boat trip down 66% if you're going on a long trip. The problem is they mostly run as intra-regional connectors so unless you're hanging around one island chain they probably won't help you.
I've got a bunch of Greece photos on my facebook. If you wanna see 'em PM me with your email and I'll add ya. Have fun!!