First off, congrats and best wishes for a wonderful life together.
My wife and I spent part of our honeymoon on Lanai last year. We stayed at The Lodge, which I think will provide you with a superior and vastly more memorable island experience than Manele Bay, which has a lovely pool but could be an upscale Caribbean resort and is not distinctly Hawaiian.
The upcountry setting at The Lodge is truly spectacular, and you get the feeling of an English hunting lodge without the animal heads. We were always made to feel special and pampered during our stay.
If you remain at Manele, be sure to take the bus up the hill to spend some time at The Lodge. If you're there mid-afternoon, you can partake in tea and pastries that are complimentary.
The good news is no matter where you stay, the restaurants are excellent. If you eat in the formal dining room at The Lodge, which may be the best (as well as priciest), men will need a jacket.
You can also spend a few hours poking in and out of the shops in Lanai City and grabbing a meal at one of the local eateries. Sorry I can't recall right now one we had lunch at, but by day it's a sandwich place, by night an Italian restaurant complete with tablecloths.
As for activities, definite must is renting a jeep in town to hit the back roads and visit Garden of the Gods. There are only 30 miles of paved roads on the island, so to see the good stuff you have to hit the 4WD trails. It's fun and not dangerous, as long as you exercise a modicum of road sense. Just be ready to pay over three bucks a gallon for gas.
But the best thing to do on Lanai is to simply relax, something so easy to accomplish regardless of where you park yourself. Enjoy.