The best suggestion - shop around. This year I was able to get a scooter for 200 kn for 24 hrs. A specialty food store in the market place, near St. Stephan, has scooters to rent - pick up some cheese , sausage, anchovies and a scooter and search out a secluded cove.
Most scooter rental are near the bus station which is behind St. Stephen.
My only other suggestion - get out early so as to see the morning light bouncing off the water
just a warning, i hired a bike from Tomas travel in Jelsa. absolutely horrible experience. bike broke down on other side of island. they refused to refund taxi and threatened to call the police on me!!! absolutely horrible people, almost ruined the trip. didnt refund me when they saw me the next day with their bike bake safe and sound. suggested i didnt know how to ride, yet i have a motorbike licence. please dont use these people. there are plently of other options. Hvar is lovely though, well worth a visit.