You would want to take water taxi or land taxi. I have only done land, you will find them all over, takes about 10 to 15 mins by cab from the port. Atlantis is the only thing really worth going out of your way for. It's very fun but pricey and I plan to skip it on my next cruise as getting there and back and enjoying it takes the whole day. I know your supposed to have a special pass you do the aquarium but I never saw anyone checking. My advice is if your not super big on waterparks(because the beach at Atlantis is really not worth it). Get off the boat, maybe do a little shopping and grab a bottle of wine to bring back or a six pack, and get back on the boat earlier to enjoy the pool while crowds are down
We took the water taxi over to Atlantis and then paid to walk through The Dig, which is a small-ish aquarium. We walked the beach, which at that time had very deep powdery sand, but did not sit there. I have heard that Atlantis cut down the number of "walk-up" items you can pay for, trying to force people to book overpriced excursions through the cruise ships, but I don't know if that is accurate right now or not. Certainly they will let you spend your cash on their food ($$$) or casino. It was neat to walk around the complex and check out the level of detail.
Walking to Atlantis would be tough because there is a large bridge that, from my understanding, is not very pedestrian friendly.
Both of the cruises we've taken have stopped in Nassau, and we haven't left the ship either time. Our next cruise does not stop there and we likely won't look to book an itinerary that does stop there in the future, because it holds zero interest for us.
If you haven't been there I think it's worth jumping in a cab and checking out Atlantis. It's not a big expense and only takes a couple hours of your day if that. I can't imagine stopping at any port I haven't been to and not getting off the ship. At least you can say you've seen it.
I envision us getting off and walking around near the port for an hour or two, being back on the ship for lunch, then enjoying the pool, etc. in the afternoon. I think this will satisfy our daughter that she can say she's been there while still spending the majority of our day on the ship.