I only mentioned the Seastar Saturday Show because it would get you off your resort and way up to the west end for zero money. (tip the driver of course)
The evening might cost you a hundred or so with buffet and drinks. Plus you get there and back safely with responsible drivers.
Late night taxis from say the Jungle to RIU could be costly if you don't know what you're doing and who to ride with, but that knowledge is yours for the asking on this message board.
That said, if you are able to change your resort without a big penalty then there are AI options like Grand Pineapple that won't break the bank and it's right in the middle of the 7 mile beach and all it has to offer. Plus a cab to the prime west end spots is cheap enough. Lots of other places have inclusive options for extra money such as breakfast every day, or bar credits every day. It's all up to you.
I wouldn't recommend you stay on the west end because it's your first time and the beach is where you want to be for that.
But once you become hooked on Negril, you might want to change it up and stay non AI and maybe on the cliffs.