We love sea days. We had a South American cruise recently with a lot of seadays. I had a mani/pedi, walked around the deck several times, read in a lounger, watched some TED talks on the TV in our room, listened to a couple of lectures, saw a movie and a show. We made a point to spend time each evening listening to the musicians--very talented and pleasant to sit there with a drink or coffee and listen. I browsed their libraries which were everywhere.
I say lots of folks getting spa treatments, spending time getting a tan. There was a group of folks doing crochet or knitting and chatting each afternoon. There was a trivia contest. I saw some folks playing cards regularily informal maybe? My husband writes. I saw others doing the same thing--journaling or creative writing maybe.
The key to enjoying sea days is to relax however you like to.