Pleasance Dome had free wifi this year - don't know about other venues apart from the book festival which also had free wi-fi but in their case it was so slow it was unusable.

Most of the big venues have had free wifi for a few years. Underbelly and the Udderbelly Pasture(Bristo Square) have free wifi as did the Assembly Rooms (George Square) and Plesance. A good number of the smaller venues, such as the Bedlam Theatre also have free wifi.

There's a lively debate here about ways of advertising the accessibility of venues:
http://ideas.edinburghfestivals.co.uk/submissions/4336-what-if-listings-in-the-programme-had-a-symbol-to-show-that-they-were-not-in-a-wheelchair-accessible-venue

Given the growing popularity of providing free wifi perhaps there's scope to publicise this better as well – whether they're on the Fringe or another festival. It would hopefully help in situations where users aren't sure if a source of wifi is legitimate, and not a rogue provider seeking to harvest information from those logging in.