I've lived on Oahu and the Big Island for all of my life (barring my recent move to Canada) so I have a decent amount of experience with the horse community on those two islands.
Living on islands is not like living on the mainland. The differences start from the origin of the resources you use to care for your horse and continue from there. Everything must be shipped over so most things cost more (hay, tack, you name it. I paid almost a hundred dollars to have a 17" English saddle shipped to the Big Island). Also, islands have only a finite amount of space, which means heavily populated islands like Oahu tend to have expensive boarding costs and less room to ride. If you ever chose to move you will need to deal with the cost of moving your horse (shipping can cost thousands of dollars and cause your horse to lose a significant amount of weight).
Hawaii can be either seem very accepting to outsiders (ohana and aloha spirit) or seem very closed off and clique-ish (family connections can seem unfairly important or give your competition a seemingly unfair advantage).
Oahu has several places that have horse communities/riding facilities. As some others have mentioned North Shore and Waimanalo. However, there are also smaller stables at Koko Crater and Kaneohe.
The Big Island is home to some massive ranches, however, this does not necessarily mean business is better. The shows are still pretty small and if you're interested in English the shows are even smaller. The paniolo-style of riding in hawaii is based on the roots of western riding, the vaqueros, so most of the riding on the big island is western. I had to search hard to find someone to teach me english riding on the Hilo-side of the Big Island when I lived there (most of the English riders are in Waimea/Kamuela/Kona). Also, being a primarily rural island the Big Island can cost you a lot in gas to get from client to client (don't forget gas has to be shipped in too so it also costs more).
Also, take into consideration what Roperchick has to say in terms of neglect and bad/behind-the-times practices. I've run into too many horses on the big island that suffered from severe neglect (elf shoe hooves, starving gangs of horses, bad breeding, lameness). This is worse on the big island as the rural-ness alows these people room to just leave their horses/do whatever they want.
I don't want to scare you off from Hawaii, but it is awful to see someone naively move over and have to listen to them realize that they've made the worst mistake of their lives and they hate it here, but don't have enough money to leave. :(
Many people move to the islands and love it here though! :) If you have an open heart and are willing to accept Hawaii as it is without complaints (or comparisons to how things are 'on the mainland') you can easily create a new family of friends in the islands who'll help you through thick and thin and help you get work by promoting you as someone they know.
Also, sorry to crush your dreams of riding on the beach, but it's illegal to do so in Hawaii...http://www.staradvertiser.com/column...l?id=120762839