There are designated no-smoking lounges and public areas, but for the most part it seems Carnival has one of the more relaxed smoking policies. As for cabins, the only ones which are specifically mentioned as "no smoking" are the Spa class cabins on the Splendor. Those guests can be assessed a cleaning fee if they break the rule. I don't use casinos enough to remember if they had a no smoking area.
I recall some hot tubs being adults-only, and perhaps the aft pool on the Legend. It has been 3 years since I was on the Legend and my memory isn't as good as it used to be.