I really enjoy going after Labor Day when the tourists all go home, the kids are back in school, and the beach really quiets down to a local crowd. The days are warm, the water is still warm, and the air is crisp with lower heat and humidity. September is perfect month to go.
Yes, September and early October is the best time ad Gunnison. I found this to be especially true before I retired and my ability to go during the week was limited. Not crowded, even on weekends. I have also been there in late October and early November if we got an unusually warm day.
A good review with photos of Gunnison Beach:
https://npplan.com/parks-by-state/new-york-national-parks/gateway-national-recreation-area-park-at-a-glance/gateway-national-recreation-area-beaches/gateway-national-recreation-area-beaches-at-sandy-hook/gateway-national-recreation-area-gunnison-beach/
Beach Parking at Sandy Hook
Sandy Hook, N.J.: Beach parking is $20 per day or $100 per season for most vehicles. For oversized vehicles (more than 20 feet), charge is $50 per day or $200 per season. Hours of collection are 8 a.m. to 6 p.m. All toll booths are cashless and accept credit, debit and contactless payment only.