Carlito's bar
Main port area.
A reader has reported discovering a great free wi-fi connection there. They don't have any computers other than maybe staff ones, so the connection is really good. He managed to get a pretty good Skype connection which is difficult enough at the best of times, never mind on wi-fi, and on a small island!
HC Andersen hotel
Phi Phi.
At certain times of the year the rooms are only 500 baht which is amazing considering you get free internet. It is said to cut out maybe twice a day but hey, we can live with that.
Phi Phi Viewpoint Resort
Phi Phi Don.
Around the open-air reception and bar. Fast enough for Skype.
D's books and coffee shop
next to Jordan's Irish Pub
Free as long as you spend THB 60 in the store. They don't change the access key either...
Ciao Bella Italian Restaurant
This
restaurant / bar with 8 rooms available for rent right on the beach has free
wi-fi from the restaurant which is accessible from the rooms as well as
while sitting on the beach or at the restaurant. Site
here.