We prefer to do Atlantis on our own and it is very easy to do. When you get off the ship walk a short distance into town and you'll see where all the cabs our. Tell them you want to go to Altantis - set a price before getting it but it should be $4 per person. They drop you right at the door! Walk through the shops and go into the Casino and look for a booth with a large blue/white glass sculpture on top. That is the temple of the moon and where they sell the wristbands. For $25 for adults (kids are cheaper - I think $19) you get a wristband that lets you walk the property (including both of the large aquarium areas known as The Dig) at your own pace. This does not allow you to use the pools, slides or beach (but neither does the Discover Atlantis excursion). When done just walk back to the taxi area (right next to where they dropped you off) and get a ride back to town.
You can take a box lunch as was suggested or if you go first thing when you dock (like we do) we've always made it back to the ship for lunch.
Cost for this would be the same as the excursion. The benefits in my opinion are:
1) You are in a van - not the water taxis that they cram people in to. A much safer ride in my opinion. I was in one of those water taxis many years ago and don't want to go back!
2) You get dropped right at the door - the water taxi drops you a block or two away (and it is an uphill walk). Since you do so much walking during your visit saved steps help.
3) You can go at your own pace. Both times we have done this we've had groups hurry past us. They don't seem to enjoy things as much as the pace is kept moving. Plus with a group you don't get to enjoy the beauty that you can see if there are only a couple of you in the room.
4) When you are on your own you get to see lots of little areas that I don't think the groups go to. There is a fun rope bridge on the far side of the property near some waterfalls that is really nice. Things like that.
If you want to see some pictures from Atlantis click on this link
Atlantis
This is from our Feb. 2003 DVC Member Cruise. Click on any picture for a larger version. Enjoy!