Club dining only applies for evening dinner, where you site at a designated table. At other times you just turn up and get seated. The Medina restaurant is open for breakfast from 8-9:30 on sea days and 7:30-9:00 on port days and 12:15-13:45 for lunch and 4-4:45 for afternoon tea. The Alexandra restaurant is sometimes used for speciality buffet lunchs i.e. Neptune (seafood) on sea days. There is also the Cafe Bordeaux, which is a waiter served lighter menu option, which is open continuously, and is used as a Marco Pierre White restaurant in the evening for a small supplement (£4.95). There is always the Orangery self service restaurant (open continuously from around 6am - 9pm) or the Sidewalk cafe for fish chips, hamburgers etc. Basically there is always somewhere open 24hours so whatever time you return you can always gets something to eat. You wont go hungry.
Agree with everthing written. I would just add that the times of the restaurant openings are published each day in the copy of the Aurora Today, which is delivered to your cabin each previous evening. And, as I have just returned from an Aurora cruise, I would recommend you try the Cafe Bordeaux for lunch, no extra charge (except for Marco's dish of the day), and the food and service was excellent.