Things have improved a lot in Taormina and many hotels, restaurants and cafes now offer free wifi.  At the Porta Messina side of town, Shaker Bar which is right beside the Palazzo Corvaja offers free wifi (and excellent cappucinos and campari!). Hostaria delle Terme and BamBar nearby are also good.  On the Piazza IX Aprile, the Mocambo bar offers free wifi and a great view alongside admittedly expensive drinks.  At the Porta Catania side of town, Vecchia Taormina also offers free wifi alongside huge pizzas and pretty good salads.

Many of the hotels also offer free wifi, Villa Belvedere and Villa Paradiso offer good wifi as does Villa Costanza Bellavista where it's even good enough to video skype.

Many other places also offer free wifi.