Dress codes are probably not enforced in the common areas of the hotel, however, as Donna stated, I wouldn't walk around the hotel in a bathing suit. The Atlantis Resort welcomes cruisers with open arms (and money), especially in their casinos, restaurants, gift shops, bars, etc. You can explore The Digs for $29.95 (last time we were there) and gamble to your heart's content. The only areas off-limits for day visitors are the pool, slides, and beach. These areas are reserved for hotel guests and day visitors willing to shell out $149/per person for the privilege of using their pool and beach facilities for a few hours.
The hotel is fun to see and children love The Digs. If you plan on visiting, just take a taxi once you exit the pier area, it's only $4 per person one way. If you take a water taxi, the walk to the hotel from the dock can be daunting for the elderly or anyone not accustomed to long walks, uphill, in hot weather.
There is a public beach within walking distance of the Atlantis Resort next to the RIU Hotel, the beach is beautiful and free.
I was just at Atlantis - the RIU beach is literally contiguous with the Atlantis beach, same quality sand and surf. If its free then by all means go to the public beach. The Royal Caribbean site lists the Atlantis day trip with a basic lunch included as $159 for adults and $109 for kids, and there is no way the place is worth that even with the aquarium thrown in. There are no guide plaques on the aquarium displays.
The "dig" is an amazing aquarium, great for everyone. You can view from inside, underneath and also see from the top, outside. The tour is guided so you can learn about the sea life you are seeing. We were there when it was feeding time, also very interesting, certainly worth the fee to get a guided tour.