I have stayed at the Atlantis several times and have done Disney cruises a lot. If you're looking for cheap at the Atlantis there are only two things I can tell you: either it's free or it's expensive. And I mean really expensive - really. If you're looking for free, the best thing to do is just take a cab and go there. Unfortunately you won't be able to go outside towards the pools or beaches without the wristband. What you can do for free is to walk inside the resort. First of all, the resort is massive. It's really three resorts, uh, now 4 resorts in one. Each tower has a separate feel to it. Royal, the tower most guests come into, has the casino and is flashy. Beach and Coral are more laid back and the new Cove is upscale, think Manhattan condo, style. Walk into the Royal tower, go downstairs. There's a massive aquarium to look at and it's free. Walk the rest of the property inside. The casino is nice. There's a lot to look at inside that's free.
As far as the Dig at the Atlantis, I can't tell you anything about that. In all the times that I've been there, we were never interested. Spent entire time outside at pools, which are incredibly amazing.
Hope this answers your question.