I say wing it --- I've done this several times --- found one of my favorite spots this way --- there are also some nice spots on the cliffs

let me dig around and see if I can "the map" of Negril so you can see all the places to stay and eat

you may also want to check out some trip reports to give you ideas for excursions, places to eat and drink

and yes I've winged it during Christmas, New Years and Emancipation --- always found a room - or a recommendation

I don't think Negril is ever "sold out" --- our preferred places may be -- but not the whole city --- and since you've never been before - you have no preferred place :-)