The good news is that you will be able to get to the NPS beaches and all along the north shore with a car as long as it doesn't rain and the car and driver is capable of handling steep grades with sharp turns. The bad news is when it rains the paved roads get slick and the roads are steep with sharp turns. By the way, the rain showers come without warning and often during that part of the year.
Here are some links to video from the On St John people that will give you a bit of insight on the type of roads you will find on the island. North Shore is actually one of the better maintained roads on the island.

http://www.on-stjohn.com/2007/10/26/jeep-cam-north-shore-road-part-1/
http://www.on-stjohn.com/2007/11/02/jeep-cam-north-shore-road-part-2/
http://www.on-stjohn.com/2007/11/19/jeep-cam-north-shore-road-part-3/
http://www.on-stjohn.com/2007/12/03/jeep-cam-north-shore-road-part-4/
http://www.on-stjohn.com/2007/12/14/jeep-cam-north-shore-road-part-5/
http://www.on-stjohn.com/2007/12/24/jeep-cam-north-shore-road-part-6/
http://www.on-stjohn.com/2007/12/31/jeep-cam-last-stretch-of-north-shore-road/

Part of the fun of visiting STJ is the driving . . . hills, blind curves and donkeys all while navigating the left side of the road. And if there is a shower it gets slippery. So let your hair down, or fly in the breeze, and definitely go with a jeep, 4WD of course.

Make sure that the rental car agency will allow you to take the car to STJ. Avis does not, I believe.

billd

As far as I have ever heard read or experienced --- HERTZ -- is the only agency that contractually does not allow their cars on the STJ ferry or STJ at all.

St. John is the island you will be visiting..."St. John's" is a city in Antigua...and greet every person you speak to with "Good morning/afternoon/evening or night"

Have fun!