Welcome to the board Kim! I hope you fall in love with Negril just as we all have.
I don't know anything about the Caves, haven't been. But we do our travel on a limited budget which allows us to go more often.
We've been to AI's in other countries, but I just find that we never left the property because everything we had was paid for and we are cheap ....... lol.
You will LOVE the pub crawl, great way to meet people and see places that you may never have even thought of stopping at.
Enjoy your honeymoon to the fullest and please take the time to explore what Negril has to offer.