Agree...Get as close to your final destination as possible. We've done similar, and while you do arrive tired, it will still be daylight when you get to HNL, and the sun does have a way of affecting your sleep patterns a bit--you'll still be jetlagged for a few days, but the sun, combined with the excitement of being in paradise, you'll most likely be fine for the short hop to Kauai.

Additionally, you will already be through airport security, most likely won't have to re-check bags, schlep back and forth between the airport and hotel, etc. Taking a mid-day 1-hour flight with 3-4 hours total travel time (to the airport early, security, waiting in line, flying, arriving and claiming your bags for the second time) does pretty much kill a whole day. If you are bent on seeing Oahu, take a later flight in the evening and see Pearl Harbor, Diamond Head and all the other great things suggested above--but I wouldn't do it, personally.

Plus, I think you'll save some money--depending on how you booked the ticket and which carrier you're on from HNL-LIH, you won't have to pay baggage fees on this short hop if your bags are checked all the way through. I think Island Air and Hawaiian interline with UA. Assuming you each have 2 bags, that's $17/bag X 2 = $34/person = a good start to a nice meal somewhere.

Similar experience, but worse. I once had to get to Shanghai. But had to go SFO-Beijing first. After much consideration, I opted to stay the night in Beijing instead of a 3-hour layover in PEK that night. After flying for 24 hours, I regretted not just getting to Shanghai that night. As tired as I was, the next day, I wasted a whole day getting from PEK-SHA, and was still awake around the time I'd have landed in Shanghai.