An article at Pocket Now details some of the reasons why municpality-provided wireless internet -- often thought of as free public wi-fi -- is a bad idea.
It boils down to two primary issues; cost and privacy. My surprise is that people were still talking about municipal wi-fi. Current wireless technology would require a lot of routers to cover an area, as well as the lines and power to run them. Cable television and phone companies already have that infrastructure built, meaning they just have to piggy-back their new stuff on top of already-built equipment. If I remember correctly the very little of my econ classes that stuck, these items are referred to as "sunk costs" for those companies, meaning they have already paid for the material.
Cities would have to buy and install the systems, which would not be free, and they would recoup expenses through one or several of their usual revenue streams like water and sewer bills, licenses, sales taxes, etc. Free, therefore, would not really be free.
Them's the breaks, kid.