Your best bet is any event sponsored by the Fanø Jazzklub, Bavnebjergtoft 7 (tel. 75-16-28-52), at Fanø. The club has various events in summer, and the tourist office keeps a schedule. Tickets cost DKK70 to DKK110 ($12-$19/£7-£11) and can be purchased at the door.
Don't expect glitter or glamour on Fanø, as virtually everyone who lives here seems to believe in honest industry and an early-to-bed kind of entertainment agenda. In Sønderho, a fun bar is Nanas Stue (tel. 75-16-40-25), which is lively and comfy with live music and good food.