Wow, this is another memory lane special. I never flew on Royal Hawaiian when I grew up in Hawaii. However, as a kid, I always wanted to fly with them because they would fly to these airstrips that are not operating anymore. Besides Ka'anapali as mentioned above, Royal Hawaiian used to fly to Upolu airport on the Big Island, literally almost at the northern tip of the island. They also used to fly to Hanalei, which became Princeville airport. They also had flights to Poipu airport and they might have had service to Hanapepe/Port Allen. Royal Hawaiian had daily flights to Hana, where the other competing airline was HA, flying CV-640s.
Royal Hawaiian's route maps and airline graphics were superb. They were all designed by Bruce Hopper Design, which was one of Hawaii's premier graphic design studios at that time.