Hi! You've mentioned my favorite place in Nassau! Here's a cut and paste of directions I wrote up a while ago. Enjoy!
This note is for people who want to just go visit Atlantis and tour the Dig, a huge grouping of aquariums. If you want to use the water amenities(ANY water recreation on property), you need to get a room at Atlantis or Comfort Suites at Atlantis. None of the Disney excursions include this either, with the exception of one tour which gives limited access to one beach but none of the other water amenitites.
To just visit is very easy to do on your own. All you have to do is walk to the end of the dock, where there are numerous cabs(minivans) with a current rate of $4 per person to shuttle you over. There are also private limos if you prefer with competitve rates.
Where they drop you off at Atlantis is where they will pick you up to return to the dock. At this point you have access to the casino, the shops, the main building of the resort.
To get access to the Dig and all the resort, simply go to the center of the Casino to a kiosk with a blue globe over it.
Wristbands for access to the rest are $25 for adults, $19 for kids 4-12, Under 4 free. This is not for access to the water amenities, as I said above you have to get a room for that.
They will give you maps of the Dig/resort and such at that point. You're now on your own to explore the resort at your own pace. The Dig is in sections spread over the resort and it is a great deal of walking. But definitely worth it. Enjoy!