There is a nice MUP on Sandy Hook, not for a road bike though. There will be lots of bike traffic, so you'll have to keep your speed down. There are roads you can wander around on the north end.
As it's going to be a hot Sunday, it will be crowded. The park road will be busy, and it's not bike friendly.
You could takea ride on the Henry Hudson trail, again a MUP, and not the best for a road bike, but it's longer than what you'd be able to do at Sandy Hook.
Or you could try the roads around Highlands, I usually don't ride there in the summer, but assume they will be crowded as well. Good Luck.