Taking the wife and 2 young kids to Miyakojima. Was told the Happy Island Miyako was a great place to stay. Which part of the island should we look for ~USD$100/night hotels?

Looking for a nice place to stay with good vibes. We're renting a car, but also like to explore the surrounding areas on foot. First time to the island, hitting Okinawa after. I have looked through the sub, but am also looking for recent experiences. Thank you.