Having done that flight a few times... I'd say rest. You will be doing the red-eye outta Hawaii. I don't know about you, but I generally can not sleep much on a plane. And since your flight probably doesn't leave Hawaii until sometime around 10pm, you probably will be up the whole day before you leave (at least that's the way it always seems to workout for me). Couple those two things together with the general PITA that air travel is these days, and I am pretty spent by the time I hit Denver. More often than not, I end up being "up" for 24-36 hours on the return trip.
So you may want to consider those factors when making your lay-over plans. (Also, don't forget to allow yourself enough time to go back through security... Although Denver's security area is relatively efficient)
On the plus side, DIA is a nice airport and if I had to spend 10 hours stuck somewhere, I can think of way worse airports.
Which island are you going to?
Enjoy your trip, I am envious since my "fun" travel will be limited this year.