WiFi service in Menton is spotty at best.  You can get a handout on free and low cost spots at the library, right next to the Tourist Office, but as of March 2012, it was out of date.  Do not depend on the library for computer use either; they have one (1) publicly available computer, which is NOT hooked up to a printer, and the sign-up sheet is always full for days in advance.  Good old Ronald McDonald off the Rue Piétonne, comes through though, with a free connection, accessible indoors or out.  And there is a new cafe across from the Office du Tourisme, on Avenue Verdun-Officina del Gusto--which has a good solid complimentary signal.  You'll probably need to buy a coffee, but they'll let you sit there for hours.  (March/April, 2012)