Herewith is a quick wrap-up from my recent trip to Northern Greece and the Greek Islands. I don't have enough worthwhile to share to write a full "Top Tips" blog post on it. I now have Greece 'complete': visited all its current 18 WHS and its 13 regions. I am glad am 'done' with it: I dislike its food (those oily fries, the cold rice, the dry chicken, lack of veggies), the infrequent public transport and its unimaginative approach to tourism. Best Greek WHS overall? I'd say Meteora.
The best itinerary
This
route posted by Kbecq is a good one. I don't think the islands and their WHS need more time. I'd stay overnight in Rhodes and Patmos as it allows you to explore the site outside of the busy hours. On Samos, I'd recommend visiting Vathy Samos as well for its excellent archaeological museum which makes the Heraion WHS come to life (more so than the site itself).
When to go
I had allocated more time to Samos & Patmos as I wanted to do some hiking as well, but the temperatures in the first half of September were much too high to do full-day hikes. Locals said that the weather was unusually hot (deep into the 30s every day).
Costs
The islands are much more expensive than the Greek mainland. I had 'given' myself a daily food & drinks budget of 20 EUR and that proved to be really impossible. I ended up on a daily average of 26 EUR. I spent 126 EUR per day in total excluding international flights – especially the moving around so much makes it expensive (I had 2 domestic flights, 2 ferries, and a car rental in Zagoria).
Digitalization
The Greeks do not seem to get excited much about digital possibilities such as e-tickets or card payments at shops. I haven't used as much cash as I did here in years. Often it is possible when you ask for it, although they still maybe only be half-working such as the boat tickets to Delos which (1) can be paid online, (2) will be confirmed by e-mail after a human intervention, and (3) you still need to go to the kiosk to pick up a paper ticket showing the reservation number that you received in the e-mail.