For the state permit you must be "actively engaged in fishing"
“Borrowed” this from another site:
BEACH VEHICLE PERMIT (New York State Parks)
PERMIT VALID FOR 4-WHEEL DRIVE VEHICLES ONLY
Annual Fee: $ 49.00 (Year 2006)
Dates of sale: January 2 – April 30, and Tues. after Labor Day – December 31
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This Permit not valid unless permittee and passengers over 12 years old, have in their possession rods, reels, line, bait and hooks or lures.
This permit allows access to designated beach areas at Robert Moses (Democrat Point), Gilgo, Hither Hills, Napeague and Montauk Point State Parks for the purpose of fishing ONLY. Specific regulations as follows.
HITHER HILLS, NAPEAGUE, MONTAUK POINT – Permit valid 24 hours daily ( VALID YEAR ROUND ).
ROBERT MOSES (DEMOCRAT POINT) & GILGO – Permit valid 24 hours daily from April 1 to 5PM on Friday, May 26, and from 12:01 AM on Tuesday, September 5 thru December 31, 2000. Effective 5 PM on Friday, May 26 to 12:01 AM on Tuesday, September 5, vehicles may enter Democrat Point before 7 AM or after 5 PM ONLY Vehicles may remain on the beach for no more than 48 consecutive hours.
1. All vehicles must be equipped with fishing equipment (as specified on front of Permit), a shovel, rope or tow chain, portable toilet, jack and jack board, approved (33-x12.5-MAX) tires, which are aired down to one-half the maximum rated tire pressure, spare tire & tire gauge to register a minimum 5 PSI.
2. Follow designated access roads to the beach. Do not exceed 10 MPH at any time. Vehicles are permitted access to fishing areas ONLY; vehicles are not permitted elsewhere in off-road travel. DO NOT DRIVE ON DUNES, WETLANDS, BEACH GRASS, BIRD NEST AREAS, OR IN SEAL HAULOUT AREAS.
3. Open fires, camping, trailers, boats, inflatables, bathing, surfboards, jet skis, SCUBA-diving equipment (except with separate permit for diving), wind surf/sail equipment, alcoholic beverages and pets are PROHIBITED. (EXCEPTION: Dogs are permitted on a 6 foot leash at Hither Hills, Montauk Point and Napeague State Parks in designated areas ONLY. Dog owners are expected to clean up after their dogs.) Tents and portable shelters prohibited sunset to sunrise. Parking is limited up to 48 consecutive hours. Barbecues prohibited at Robert Moses State Park.
4. Beach Vehicle Permits also allow all privileges of Sport Fishing Permits which are valid April 1 – December 31 for after sunset parking for the purpose of night fishing ONLY as follows:
CAPTREE – Main Field and Overlook Field
HITHER HILLS – except Memorial Day to Labor Day
JONES BEACH – Fields #6, #10, West End #2 and Western Boat Basin
MONTAUK POINT – Lower Parking Lot ONLY
ROBERT MOSES – Field #2, Field #3 & 4 from Sept. 15 – Dec. 31 ONLY
SUNKEN MEADOW – Field #1, Field #3 – Sept. 15 – Dec 31 ONLY
5. This permit is valid ONLY far vehicle bearing license plate number as indicated and is non-transferable to another person or vehicle. There will be NO REPLACEMENTS or REFUNDS FOR LOST, STOLEN AND/OR REVOKED PERMITS. DUPLICATE PERMITS WILL NOT BE ISSUED.
6. Environmental conditions may require the temporary or permanent closure of all or part of beach areas accessed by this permit.
Violations of any condition of this permit or of any rule of STATE PARKS or of the Long Island State Park Region may result in the immediate revocation of this permit (NO REFUND) POSSIBLE ISSUANCE OF A SUMMONS.
information courtesy of : 4x4 permit beach access
For the Suffolk county permit you must first purchase a green key before you can get the permit. Permits are available now.
Sorry to just post links but these should answer all your questions.
Good luck and have fun out there