We'd like to fly into New Orleans early before our cruise which will depart at 5pm. Is there any place we can leave out 2 carryons so we can tour the city?

customs/luggage check in are at the Port on Julia Street.
cruiscritic.com for ship reviews and details.
neworleansonline.com

Typically, you can check you luggage at the cruise terminal as early as 10am. Once you check in (check both yourself and your luggage in), then you can just head over to the French Quarter and walk around. Just be careful that you are back to the ship at least 90 minutes before departure (the ship will tell you precisely when you have to be on board).

If you have time, I'd go the day before. There's a lot to see and do in NO.

Thanks. Have been a couple of times before, but want to fly in there very early in the day to be in town in time.

New Orleans is a great city to visit and eat in. If you haven't been there before you really ought to consider going in a couple of days early.