Flew into Santorini and stayed a week. You can do so only outside the mai season, until October you can only park briefly to load/unload passengers as they have limited number of stands. You can debate the need for a stand for light GA, but I’ll let AOPA Greece argue on our behalf, they do an excellent job. In the case of Santorini, tarmac is pretty limited. Not sure if the military part if the airport is still used (didn’t look like it), but an entrepreneural approach would be to set up a GA terminal in that end and have the private jets fly in :-)
You need a handler and it’s expensive. I went with Skyserve where AOPA Greece has negotiated very favorable terms. It came to 463 EUR for an SR22 for 7 days, much less than the non-AOPA offer I had from another handler of more than 1000 EUR. It was quite complex to negotiate the whole thing and AOPA was very helpful in helping me point out the flaws in the initial decline – they assumed that I needed a roll-through stand. Note that the availability of a tow bar was a big thing in the negotiation of the parking, as they needed to be able to move the plane. Once we arrived it was all very pragmatic and they advised me to put the brakes on, they would just call me if they needed the plane moved – simples !
As there is no GA terminal, Skyserve will need to drive you the 20 meter to the terminal in a huge bus and will meet you in departure as you return and take you through security. We almost got out lunch and drinks taken away by security, until the handler put them back in their box in Greek :-). Really good service by Skyserve.
Note that there is no AVGAS on Santorini, but it’s an international airport, so if you have the range (or burn Jet) you can go direct to Santorini.
What does one do for one week in Santorini?
Did you post fees to http://airports.euroga.org/
You can do lots and lots in Santorini. It’s a beautiful island. You can also take a trip to the inner bit of the volcano. And boat trips to Paros, etc.
It’s just a bit pricey and at times past was a giant tourist ripoff – not helped by the 4 figures per day of old ladies, discharged there for a day from cruise liners, spending their widows’ inheritance 
although I reckon the place is much quieter now so it’s a good time to visit. In fact it’s a great time to visit lots of places, and doing it by GA avoids the airliner infection risk.
When I went, 2005, you could stay as long as you wanted and it cost peanuts. Fraport took care of that 
I think one can avoid dealing with Santorini Fraport using helicopters
