Check your paperwork. It may be possible that although the ship departs at 10PM, you may need to be on board by a time much earlier than that.
This is important! Do not "miss" the ship.
If I were in your position, I would arrive at the pier at 11AM and board as soon as possible in the early afternoon. This gives you the time to check out your stateroom and your table assignment in the dining room. Once you are settled you should be able to leave the ship again to tour the area. But do not take my word for this leaving once you are "checked in".
I've been to the San Juan area many times---there is a lot of shopping to do, but perhaps not much else on the day of sailing.
May I suggest that you see what you can of San Juan on that Saturday that you arrrive and leave Sunday for the enjoyment of the Advenrure----settle in and spend the time enjoying the Solarium Pool.