The island of Kos is part of the Dodecanese. It is the third largest of this group of islands and the second most popular and touristy island after Rhodes. It is located between Kalymnos and Nysiros. It is very well organised and has everything in terms of tourism infrastructure.
If you are looking for peaceful beaches, try Lakkos, with cedars and dunes, Agios Fokas with its dark sand, or Thermes.
Kefalos Bay has a number of good beaches: Camel, Paradise, Polemi, and Psilos Gremos.
Kos is a very safe area and should not be a major problem for travellers. Just take normal precautions.