Yes, the restaurants and grill remain open. The hours will be posted in the daily newsletter. Sometimes the times might shift a little, for example if there are lots of tours coming in late.
You will find organized games of Trivia, board games, scavenger hunts, etc. while in port. We try to go to all of the games, and rarely get off the boat in some ports, so we enjoy the activities. You will notice that there are not as many offered as the sea days, but if you look, they are still there.