Have been on the Zenith for a 14 night Caribbean cruise in february 2005.
Smoking was for us one of the mainproblems.
It is permitted in the pool area on starboardside (hope I´m not wrong) and on all open decks.
When you leave the Selfservice-Restaurant you have to walk through a lot of smoke. And its difficult to find a place at the pool, without smoke.
It´s also allowed in the casino and some parts of the bars, but not in the dining-room.
I hope, you will enjoy your cruise on the Zenith and hope for you, that they have refurbished some places on the ship.