In my opinion the big hotel chains don't have the nicest properties. On Oahu I prefer to be slightly away from Waikiki beach, my favorite is the Mandarin Oriental and its the only place I would consider staying on the island. Does Fairmont qualify as a "big hotel chain"? If so then I would go with them on Maui and the Big Island. Four Seasons also has hotels on both of those islands. Starwood has great properties on Kuai (The Princeville) and Lana'i (The Lodge at Koele and the Manele Bay Hotel) but the remainder of their hotels are mediocore at best.