I explored the caverns and in the part just inside the door from the House of Games, I found what looks like Hook's quarters and found a fancy looking key in one of those rooms.

The Fellowship guy in Buccaneer's Den told me where the Black Gate is and that Hook likely kept his key in his quarters.

I explored the rest of the caverns but didn't find Hook.

Is Hook somewhere in the caverns?

Thanks much for any advice anyone has.

Thanks guys!