If you want to inject a little more culture into your trip, put Kostas and Angela Mavrikis Museum of Alonissos on your must-visit list. Check for guided tours or just wander around at your own speed.
To visit this museum, make your way to Patitiri. There are plenty of other things to see in the area, including Chrisi Milia Beach, Patitiri Harbour, and Leftos Gialos.