all of the restaurants and dining rooms are open for dinner, its open seating for the first night in the main dining rooms, dress code is casual. You can store your luggage under the bed or in the closet, if you have a huge bag, your room steward will take the empty bag and store it for you.
As I was told emphatically, casual does not mean jeans. Wear something nice enough to be admitted to the dining room in case your luggage doesn't arrive in time. Or you can go to Horizon Court where jeans and shorts are always welcome.
We did not get our luggage until 9 p.m. on the first night on the Golden out of San Juan on 7/4 (TSA inspected our bags). The dining rooms were open and we had our shorts and polos on. The staff was really cool, understood that we did not have our luggage and we ate a nice prime rib dinner the first night. Saw lots of people in their travel clothes that night, too. We dressed appropriately after that for every meal, but I did see a guy in shorts and a t-shirt on the last formal night eating. Nice to have a jacket and tie on and see a scruffy looking guy next to your table chowing down!