I got the chance to hike with my dog at Cheesequake State Park in Old Bridge, New Jersey in November of last year. It was a windy day and the trails were pleasant enough, though perhaps not so interesting that it warrants a return trip.
Unfortunately I'm getting around to writing this much too long after being there in order to provide specific trail information. Though I suppose that is a lesson for next time! After getting through my queue of back logged "Hike New Jersey" posts that is!
I surely went on a weekday, as those of you with reactive dogs of your own will understand. I do not recall encountering many people. There is something to be said for hiking mid-week in the Winter. The lake was an interesting spot that surely fills up in the Spring and Summer months.
It's a nice state park worth checking out if you have the time and inclination (and if the drive isn't terribly far), though likely not a desirable spot for more adventurous hikers. If you also have a reactive dog, I recall there being adequate space to pull over and let others pass (for the most part). Though like all places, there is always opportunity to find oneself in a tight spot with nowhere to go, making high value treats a must during all outdoor excursions.
Like many of my hikes in New Jersey, I remember relying njhiking.com for trail advice, reviews, and directions!