My favorite part of HHI is the beach at sunset. (no, the sun doesn't set over the water as this former west coaster finally noticed....but the reflection on the water and clouds can be stunningly gorgeous).
How about bringing a blanket, a picnic basket of delectable goodies, a bottle of champagne (alcohol is officially not allowed on the beach but no one will care--don't forget the corkscrew), 2 champagne flutes for a private picnic and walk on the beach for the two of you. Any wife would LOVE to be surprised this way, trust me.
There are also sunset dolphin cruises, but more people will be around.
When you get there, pick up the golfer's guide, a free booklet listing all the courses and prices. Tee time shouldn't be too difficult to get.
Have fun!