They have 2 hotels at the Mauna Lani Resort. The Mauna Lani Bay Hotel and the Fairmont Orchid. Both play over the two Mauna Lani courses.
The Mauna Lani Bay Hotel is a little bit better and more expensive. Both are very very nice.
Definately play Mauna Kea if there. Mauna Lani is beautiful, but rather standard resort golf design.
Yes and Kapalua Plantation is on Maui, not the Big Island.