Hotels usually have a full legally regulated rate (the one posted on the inside of the door inside the room), a walk in rate (what they charge if you just show up) and an advance booking rate.
The full rate that is posted is usually equal to the walk in rate during peak season and, with the exception of a holiday surcharge (NYE, Xmas, etc), is the highest amount they can legally charge for that room.
The walk in rate varies depending on the season, during shoulder season in Hawai'i it could be quite a bit lower than during peak summer season. While this rate is usually a set amount, most front desks have some leeway to discount that rate if the hotel has low occupancy.
The discounted rates offered by the hotel for advance bookings through its own website vs the rates offered through OTAs, like Agoda or Expedia, etc are becoming more equal as time goes by. The primary advantage of OTAs is being able to look at multiple options on one page AND since OTAs have blocks of rooms they committed to, they will offer the same discounted rate right up to check in day.
Hawai'i is busy but not totally sold out, with the exception of the peak seasons, you can find rooms available in most areas upon arrival. And even during peak summer and the new year period, there will be some room to be had somewhere.
Personally I would book my first stay before leaving for the islands, just for the ease of arriving and relaxing instead of hunting down rooms. Then as you piece together your next location, get online with the OTAs booking.com, hotels.com, agoda.com etc and see what they have available. If rooms are available you can book them right up until you arrive at the hotel. You can also use the price the OTAs quote as bargaining material if you want to walk in and book direct with the hotel.
And if you spot a really cool hotel while wandering around but the front desk tells you they have no rooms, check with the OTAs as they may have space in their blocks still, which the front desk can't access to sell direct.