i havent travelled directly to greece, but i was there this summer while backpacking.. each island has its own allure but they are all amazing in their own way. For a honeymoon, you will probably like santorini the best.. beautiful cliff side towns with nicer hotels and good food would make for a really romantic place to be. Personally I felt the laid back atmosphere of the island Syros was my favorite. It has a couple of really nice beaches, great food, friendly people, and was just a really relaxed place to be alone with my girlfriend. It is not as popular an island as the rest, but maybe thats why i liked it... it wasnt too touristy.
buy a travel book and see what interests you... there is an island for everyone
or island hop like we did!
edit: as for making travel arrangments, there are direct flights from london to the main islands atleast once a week during the summer months. once you are in the islands your best bet is to ferry around to others, as they run daily. They can be expensive though if you want a private room. accomodations can vary quite a bit.. you can find a nice bed and breakfast for 15-20 euro per person.. or spend hundreds of euro for the 4 star treatment. for last minute hotel deals, check
www.booking.com. thats what we used while traveling around europe and got some great deals.