Your orders should tell you. It will say something like military lodging/quarters authorized or something like that. You will have to try to contact Tripler or Schofield Barracks first to get lodging. If they do not have any - then when you arrive they will stamp your orders with a "statement of non-availability" so you can go to a different hotel and get reimbursed.
Make sure you check with Schofield Barracks lodging facility, not Tripler. Even though your orders say Tripler, you will most likely be spending your time at the Schofield clinic. When you call, give them your stay dates, and they will tell you if lodging is available or not. If not, they will then give you a "statement of non-availability control number". You will still need to get your in-processing paperwork stamped once you get there, but once they tell you your SNA number, you can then book a hotel wherever you like.
Make sure you go on line to check per diem rates and get a hotel room at or below the per diem rate. Most hotels know the per diem rates and have a "government rate" that is the same as the per diem rate.
When I did my ADT there, I stayed in Kailua. It was a 40 minute commute each way, but the nights and weekends were awesome! The best 5 weeks of dentistry I've had yet.