I've stayed at the Turtle Bay (once a long time ago), and The Royal Hawaiian twice (once recently). I remember Turtle Bay as being ok, but kind of forgettable. Pretty views, but I wasn't blown away. And it is very far away from Honolulu, if your goal is to be close to the city.
I loved our first visit (a long time ago) to the Royal Hawaiian - the history of that hotel is what drew us in and charmed us. We went again in 2020 and we both agreed that that was enough. Everything around the hotel is so built up now that there's a real feeling of being kind of hemmed in.
Honolulu is so crowded that it's hard to imagine what it would have been like to arrive by boat in the 1920's, or to be in the Navy in WWII and stay in the Royal Hawaiian for one last fling before being shipped out to the war in the Pacific. There are plenty of other places in Hawaii that are much prettier and more relaxing than downtown Honolulu.
If it were me, and I was going to be in Honolulu anyway, I'd stop by the Royal Hawaiian just to walk around and maybe go to Dukes next door to have lunch or a slice of Hula pie. I'd just pick somewhere else to stay.