There are trails across the street but they are not "legal" until you get to the marked loop (pink blazes) near the camp site. A large portion of that property is Monmouth Cty. land. There is some fun stuff over there, go out and explore but stop at the Parkway.
The trails over there can be great, super-fast but less well marked. I would recommend finding someone in the parking lot who knows them and have at it. There used to be some interesting slightly more tech stuff over there, but that seems to have been removed. Anyway have fun
That side of Allaire is called the campground side. It's a great place to ride but be careful because alot of trails have some really steep features with sharp turns at the bottom. Hook up with some guys who have ridden there before to show you around.