Port Royal is an amazing experience!!
The trip would be more relaxing if you can stay a night or two in Kingston or somewhere nearby. It can be done in one day albeit a very long travel day (approx. 8 hours of total driving)...I would combine it with the Bob Marley museum and/or Devon House.
Getting from Negril to Port Royal is going to depend on your comfort level.
The easiest and most comfortable way to get there, is to hire a driver from Negril to stay with you the whole trip.
A more affordable option would be to take the Knutsford Bus into Kingston....a Kingston driver that you've arranged ahead of time would pick you up and drive you around town. They'd return you to catch your scheduled Knutsford bus to Negril later in the day.
However you get there...if you'd like to see another side of Jamaica and experience a bit of the history here...it's a place I think everyone should take the time to visit!!