Wave energy is of interest for regions with high wave power potential, as well as for regions with modest wave power potential such as the Adriatic/Mediterranean coastlines and islands. In the present paper, the possibility of integrating a wave power farm with the power system of an island in the Adriatic Sea, combining the wave power with a battery energy storage system (BESS) and solar photovoltaics (PVs) is explored and its impact on the local weak low voltage grid is investigated. The load profile is typical of the demand (consumption) of an Adriatic island, in which the demand substantially increases during summer (the tourist season). The wave power technology is a point-absorbing wave energy converter (WEC) with a direct drive linear permanent-magnet synchronous generator power take-off device. Wave power farms (WPFs) consist of two to ten WECs. In this study, we show that the integration of a WPF consisting of two WECs into the grid is optimal and helps to reach zero grid exchange, and a BESS reduces the intermittency of the power flow into the grid. Since a potential wave power farm is to be installed in a populated recreational area, the technical study is complemented by discussion on cross-cutting aspects such as its environmental and social impact.