Temperature in the Ionian sea does not fall below 14 grades Centigrade, some people swim in winter. There is a proverb that residents of Taormina go bathing only after the holiday of the patron saint St. Pancras (July, 9th).
Good bathing weather may last till November, but there are years when showers start at the end of September. I think the best time for a beach holiday is the last week of August and the first week of September.
There are several beaches in Taormina - Mazzeo, Villagonia, Spisone, Mazzaro, Isola Bella. The most picturesque, number one in the top of the most photographed places is Nature Reserve Isola Bella. The beach Mazzaro with five-star hotels is adjacent, here you can rent a boat. Mazzaro and Isola Bella can be reached by the cable car (Funivia - in Italian). When in the low season the cable car is closed, there are small orange buses that can take you to the historical centre.
There is a convenient parking place near the cable-car ticket office, where you can park a car easily even during the peak season. Many people in August leave a car here and go up to town by "funivia".
The longest beach in Taormina is Spisone, it can be reached by the blue "Beach bus" which you can take at the bus stop "Fermata San Pancrazio" near the Porta Messina. The bus-schedule, funivia time table may be viewed on the A.S.M. website . At Spisone do not miss the opportunity to dine at lido Re del Sole with an amazing sea-view, fresh fish is cooked by Valentino. It is better to book a table because local people adore this place.
All beaches of Taormina are shingly, so it's advisable to buy special rubber slippers either in the shops in the center or at the beach (average price is 8-10 Euro).