I'm going to try to do the Chef's Table on my next cruise in October; the word is you have to make your reservation as soon as you board the ship--go directly to the Maitre d' or call the dinner reservation line--space is very limited.
You should also try Sabatini's and Crown Grill at least once during your cruise; there is an extra charge--but well worth it.
There should be two wine tastings: one is a kind of introduction to the art of wine and the second is for premium wines.
There will also be a cooking demonstration at some point, and of course an opportunity to buy a cookbook autographed by the Master Chef. There should also be a galley tour.
Watch your Princess Patter, the daily newsletter, for the dates and times of these extra activities.