I literally just did this (went to Aulani then flew to the Big Island three days later). It is doable, but very very easy to screw up or end up spending way too much money. Here are some flags to make sure everything goes smoothly (and free of charge):
1) Don't got to the closest testing site, go to the testing site that will make the 72 hour state requirement every time. Many testing sites fail on the 72 hour interisland turnaround time and will tell you they can't promise hitting the deadline. For example CVS/Longs 5 miles away from Aulani is is a popular option, but also notorious for missing the 72 hour deadline and pushing you into quarantine.
2) Many testing sites charge $200/test and will code it so it isn't reimbursable by insurance.
3) Some testing sites refuse kids under 10-12 (e.g., CVS), but all kids over 5 have to have a test. So, if you have kids under 12, you need to make sure that the testing site takes young kids.
4) Some test sites produce reports that can't be read by the automated State of Hawaii Safe Travels system, potentially complicating your travel and pushing you into quarantine.
After many hours of research, the only testing brand that hit all four criteria (free, kids under 12 okay, basically garuntuees the 72 deadline, produces a test report that automated State system reads) is Walgreens. We used Walgreens, got the PCR test results back in 40 hours for all kids and adults, got them auto approved by the State website, and it was free for all. Use Walgreens.
Now, there are two catches, 1) Walgreens appointments fill up fast (other inter island travelers are onto the Walgreens secret) and get posted at different times by different stores. They get posted about 48-72 hours ahead of time, but you have to keep updating the website and grab appointments ASAP. We ended up driving all the way to Kailua for our appointment, but it was a fun drive and we had some awesome breakfast burritos over there. There are five closer than Kailua to Aulani (i.e., in Uber distance), but you have to snag the appointments super fast. 2) I think Walgreens still requires you to pass screening questions to get tested (one of them is super broad like "have you interacted with anyone that had Covid symptoms in the last 14 days?") so many qualify. Not sure what happens if you don't meet any of the screening criteria.