This paper aims to investigate the development of a floating artificial sustainable energy island at a conceptual design level that would enhance the energy independence of islands focusing on a case study on the island of Crete. This paper provides a baseline assessment showing the immense potential of wind and solar energy in and around Crete integrating the third significant renewable energy source (RES) of ocean waves into the energy island. The selection of the best location for the floating offshore platforms that compose the energy island is addressed through exploiting the great potential of the above-mentioned RES, taking into consideration criteria with regard to several significant human activities. To this end, the concept of an innovative floating modular energy island (FMEI) that integrates different renewable energy resources is proposed; in addition, a case study that focuses on the energy independency of a big island illustrates the concept referring to the substitution of the local thermal power plants that are currently in operation in Crete with sustainable energy power. Although focused on the renewable energy resources around Crete, the work of this paper provides a basis for a systematic offshore renewable energy assessment as it proposes a new methodology that could be used anywhere around the globe.