Giardini Naxos is generally a safe place for solo female travelers. The locals are friendly and chivalrous, and crimes especially directed towards tourists are infrequent. As in any destination, there is a certain degree of caution that should be exercised - it's wise to avoid secluded areas late at night and keep an eye on personal belongings, especially in crowded places. Use common sense and take basic precautions, and your trip should be safe and enjoyable.