I have been lucky enough to go there most summers for a week or so with my family. My jeep is plastered with oversand vehicle permits from when my mom owned my Jeep.
It was great 10 years ago, but now it sucks.
Smith Point is always closed because of stupid birds and landowners getting mad about parties late at night. Great Point is nice but it requires a separate sticker that goes around $150, and regular Nantucket Beach is around $150 as well.
There isn't any real offroading, all the "trails" are soft sand and terrian that a Subaru can do. We brought my moms Toyota Camery to the top of Altar Rock once.
However it is very fun driving out to the beach, taking the surfboards off the top of the car and going in the water. But going over there is not practical anymore, it costs around $400 to bring a car over, and that is about 6 months in advance. You will have to pay at least $2000 a week for a cotage, and thats for one with a single bedroom and rats crawling around.
The island is a great place that everyone should go to but I would not associate it with offroading. The beaches are much better!