For starters, you may have problems with a one way ticket to Athens. When you get to Greece, customs are not going to be very excited that you have no return ticket from Greece, and they will ask what you are doing in the country. Make sure you have your return ticket from Heathrow (or wherever you're flying home from) to show to customs to prove that you are, in fact, leaving the EU before 6 months.

Bring stuff to read, you'll need it.

Don't give money to beggars.

Book accommodations in advance.

I think finishing in London is smart. There's nothing like being back in an English speaking country after a trip to the wild, and weird, continent. It's like being back in comfortable, familiar New England!

Have fun. Maybe I'll bump into you on a train somewhere.