If you are talking about the Atlantis Hotel, it is in Nassau and the cabs are readily available just as you walk through the security gate in town off the ship. If you are talking about the Atlantis subs, they are in the Bahamas and you can walk to their stand. Just walk to the right as you get off the pier. Their shack is about 200 yards.
I haven't been to St. Thomas, but I pretty much go to Nassau once a year by cruise ship. Atlantis is a popular destination so you'll have absoutley no problem getting there and it's very easy and pretty quick as far as travel time. You can get their by taking a boat or a taxi...you can not walk it as it's too far from the cruise docks for that. It's around $7.00 per person each way (I think, if I remember right) no matter which mode of transporatation you take. I like to take a boat to Atlantis on Paradise Island and then a taxi back. I once even took a limo back (either way the resort has a valet that will help you take either a taxi or a limo, so you don't have to worry about finding one yourself). To find the water taxi (boat) head over behind the shops just off the pier to you right...just keep following the water. For a taxi just head for the main strip (just past security at the the end of the pier). More than likely you'll be stopped half a dozen times after you get off the ship anyway with someone asking which mode of transportation they can help you with. I love Nassau, so have fun!