Hawaii is expensive. You need airfare, room and car. After that, you can eat frugally, or not. You can buy souvenirs, or not, and you can do free things (beaches, hikes) or expensive activities (boat trips, zip line, luaus). If Hawaii is something that you've wanted to do, price out a trip with the prize and price it out going on your own. The best airfare we ever got was $700 round trip. Some people have good luck with Alaskan airlines, but they didn't have flights that worked for us. We usually fly American into Lihue.
Depending on how long the prize is good for, you might be able to save money and do the four days on Oahu combined with a week or so on another island (Kauai, Maui or Big Island). For me, four days on Oahu would be more than enough.
There are condos, VRBO and lots of other options. We did Priceline for Waikiki and got a good deal.
You will really need a car on any island. Too much beauty to miss. If you want a resort-only vacation where you don't need a car, go to an island in the Caribbean where safety might be an issue off the resort. Those are pretty cheap.
I've been to Hawaii many times. The shortest trip was one week and I vowed never again for that short of a trip (I'm also east coast). As a pp stated, day one is eaten with travel. With time change from east coast, you'll be getting up early and struggling to stay awake the first few days.
Check out TripAdvisor for lots of good info.
Good luck with your decision.