While I felt that Hakodate was a strange place in Japan with its nods to western influence dotted in the city, the island of Okinawa is another strange location within different context in Japan. The tropical island setting is unlike any other place I've visited in the country. Housing United States Air Force, Navy and Marines Corp bases throughout the island, there are plenty of non-Japanese living their daily lives, going shopping, driving around in Y-plate and A-plate cars, and hitting up fast food joints all over. Add in the masses of tourists visiting from neighboring parts of Asia and the location gives off the vibe of being the most internationalized location in Japan just by sheer number of non-Japanese seen and heard.
Rental car companies here have special stickers placed on the back windows of non-Japanese tourists, "warning" others that the person driving the vehicle is a non-native visitor. While it's possible to get around and see the City of Naha without a car, you're left without seeing some amazing coasts outside of joining a charter bus and being rushed around every 20 minutes by a group leader.
The best itinerary for Okinawa that I can give is to maybe stay a night in Naha, the the beginning or end of the trip to give two days of sightseeing and shopping in the city. Then make the majority of your time at a hotel or hostel away from the city and traffic to spend leisurely time on the sand as much as possible. With a car, you're free to wander up and down the coast looking for a good beach to stop at and the traffic isn't too bad during the afternoon. Also, if you make your way up to the City of Nago on a leisurely drive, stay the hell away from the Nago Pineapple Park. That shit is not worth anyone's time.
It's probably best to do the Naha touristy stuff last as traffic on the 58, Okinawa's main traffic artery up and down the island, is a mess during the morning and evening when everyone is commuting to and from work. If you have to jet out in the morning, depending on where you're staying the night before your flight, you'd better be on your way to the airport hours before. We stayed at a resort in Onna-mura, about an hour+ drive from central Naha, and the drive to the airport took over over hours with the weekday morning rush. Being closer to the airport in Naha will save you the stress of being stuck in traffic wondering if you're going to make your flight.