You should have almost free reign of the entire ship. As long as he's with you, you'll be able to go in all crew areas. Hang out in the bar or have dinner in the officer's mess. If you want to eat in the passenger's dining room have your boyfriend fill out the paperwork for the two of you to do so prior to you coming, or go and see the matre'd first thing that week. You'll definately want to eat with the rest of the passengers. At least the majority of the cruise and he can go with you as long as he gets it approved before hand. It's no big deal, just requires a form to make sure that no one (himself or the matre'd) gets in trouble.
As for the time when he is working, you can do whatever you want. Lay out by the pool and get some sun or get involved in the activities on board. There are plenty of people to meet on board and i'm sure you'll be fine. A lovely lady alone on a ship. I'm sure you'll have no problem finding people to talk to. Good luck and have fun. Maybe spend some of that down time to attempt to learn Italian. It will make this relationship much easier, but maybe not as exciting!!