the policy varies from line to line but on average there is no smoking in any of the dining rooms. Most ships have designated smoking areas. Smoking is allowed in the casinos and bars, and in your stateroom.
You can find each lines policy on their web site, usually under FAQ section.
Normally smoking is permitted on the port side of the ship in public areas as lounges and open decks. No smoking in the buffet or any dinning area. Guest relations area, shops and theater is no smoking.
__________________ Ready to Steer towards another cruise
No ships that I know of, other than Regent Seven Seas, allow smoking in any of the dining venues.
Carnival now has a couple of totally smoke free lounges on all of their ships, you'd just have to find out which have that designation.
RCI's Radiance of the Seas had the most restrictive smoking policy I've yet encountered (though I hadn't experienced the same on previous RCI cruises). On that ship, aside from the casino only 2 of the lounges had a smoking section, the rest were designated totally non smoking.