Fortunately, I travel with my best friend, whom I also happened to be married to, so I don't need local tour guides to connect me with activities that I could get banned from Scuba Board for mentioning in greater detail.
When my wife and I travel, we enjoy finding local hikes to take, in order to see more of the surrounding area and scenery. We enjoy geocaching, and someone operating a local dive resort could easily place a few geocaches in the nearby area for cachers to find (if there aren't already plenty of caches in the area).
Local performing arts are of interest, especially in areas where the culture is different from what we're used to. Information about other local artists is also worth having handy (painters, sculptors, writers, etc.).
One thing I think would have been cool over in Fiji last year - having a large monitor computer system in the common area, so divers can review and share photos and videos taken that day. Sure, we can show others what we have on our cameras, but those little LCD's on the cameras themselves aren't always the best for see how the shots REALLY turned out.
I enjoy taking a kite or two along, and seeing if I can find a good location to spend some time flying one of my kites. I have a parafoil stunt kite that packs down very compact and lightweight, so it isn't a big deal to bring along.
If you're talking a liveaboard or a remote location that doesn't have much access to outside activities, then I suggest packing some easy to play games such as "Apples to Apples." This game, especially, is great for helping people get to know each other. It's fun, takes almost no time at all to learn, and can be played for as short or long a time as you want. Plus, it doesn't require any other accessories, and even if you lose a few of the cards, it doesn't render the game unplayable.