Yes, I do have one... and in May, you just walk up, there will be rooms. Stayed there in 2007, I got it from a friend. It is called "Enomeni Evropi" (also written on sign "United Europe". (sign also says English Spoken). 35€ per night, room upstairs with lovely balcony with a view of the hills). It is run by a couple -- German?? Josh & Birgitta -- about 70, I think they moved to Kea 35+ years ago.
To get there, you get off ferry and walk along the water to the LEFT of the port as you face inland .... maybe 300 yards; you will come to a sort of "supermarket' (small food market) and on the road by it, you walk inland about 50-75 yards, on the far side of a paved dry-stream bed . The Place has hedge & flowering bushes surrounding it, rather attractive.
The "high town" in Kea is fascinating... you can take a taxi up there for €5 or so, To get a taxi, go to a taverna on the waterfront, and ask there how you get a taxi. Then walk down on the flagstoned donkey path.... a terrific walk ... AND I met an old Geezer with a donkey, he was picking walnuts off the trees. It felt like the 1950s or something -- until I ran into a construction crew! There is probably an ugly new fancy hotel along the road now.
THeres a nice beach about a km to the right of where u stay, away from port. SUnloungers but they don't charge in May. Do you like hikes?? Here's a good website describing all the island hikes: http://www.cycladen.be/KeaEng.htm
PS: tavernas in port are mediocre; ask around for the best places.
