JoeVa - I add my congrats on the impending marriage.
Murph stated it pretty well. But just to expound - the route taxi system in Negril makes it so that a private taxi is rarely needed just doing things IN NEGRIL.
The few exceptions that come to mind - are a big grocery trip, or if running errands and have several stops - other than that, rarely needed.

You will need, and should pre-arrange, your Airport Transfers. Many recommended here - Clive's, Rocky, etc. just do a quick search on here for "Airport transfer".
Also, you will need private transportation if you take any of the excursions out of Negril - like to YS Falls, Appleton Rum Factory, Black River, Roaring River, etc. Again, a few searches will quickly give you a long list of safe recommendations.
Other than that - you'll pretty much be throwing your money away with a Private Driver just bar-hopping or going to restaurants or attractions just in Negril.
If we haven't convinced you yet - I'd suggest you wait until you are here, and see what we mean by the route taxis - then decide.

Do some searches on here if not familiar with route taxi - but really quick is just $100JA/person (about $1.15) anywhere along the beach to town center, another $100JA/person anywhere along Cliffs to town center. You just watch for them - hail, hop in, hop out, pay the $100JA and tip if you want.

Enjoy!