However, with a permit and according to town guidelines (provided below) you can host a bonfire.

It is crucial to the environment that you contain the fire in a metal holder and clean up everything that remains and not simply bury the fire in sand as it is not only illegal but causes the carbon embers/remains to leach into the water. Increases in carbon in the water change the acidity of the water. More acidic water can dissolve shells of marine organisms (clams, oysters, crabs, etc.) Increased carbon also acts as fertilizer for water-based plants such as phytoplankton and algae. This can lead to the growth of lethal algael blooms and red tides which render the water un-swimmable, un-potable, uninhabitable for fish and marine-life, and can even release neurotoxins into the air that can cause paralysis in humans.

For more information on the carbon cycle see: http://earthobservatory.nasa.gov/Features/CarbonCycle/page5.php

EH:
§ 141-18. Penalties for offenses.
Failure to comply with a provision of this ordinance or regulations adopted pursuant to this ordinance shall be punishable by a fine of not more than $250 or by imprisonment not to exceed 15 days, or both, and each day such violation continues shall constitute a separate violation.
§ 141-19. Beach fire regulations.
A. The following regulations shall apply to all beach fires within the Town of East Hampton:
(1) Beach fires shall not be started or maintained less than 50 feet from any beach grass, vegetation, tent, fence, building or permanent structure, nor within 100 feet of any lifeguard stand. Should there not be enough beach to comply with the fifty-foot setback, the location of a beach fire may be reduced to 25 feet from any beach grass, vegetation, tent, fence, building, or permanent structure, but in no instance may a beach fire be located less than 25 feet from any beach grass, vegetation, tent, fence, building, or permanent structure.
(2) Only clean wood shall be used for a beach fire. No chemically treated wood, or wood with paint or nails, nor wood or plastic pallets shall be used.
(3) Metal, plastic or glass shall not be placed or thrown into the fire.
(4) No beach fire shall be left unattended.
(5) A Fire Marshal, Marine Patrol Officer or police officer may require that a beach fire be extinguished when deemed to be dangerous due to wind conditions or size or whenever atmospheric or other circumstances present an increased fire hazard.
(6) No beach fire shall be started, kindled or maintained if the prevailing wind velocity exceeds 20 miles per hour. However, the Fire Marshal, Marine Patrol Officer, or police officer may exercise discretion in requiring that a fire be extinguished when wind velocity exceeds 10 miles per hour.
(7) A pail or bucket of water must be kept within 10 feet of the beach fire at all times.
(8) No beach fire shall be started, kindled or maintained prior to 5:00 p.m. and must be fully extinguished prior to 11:59 p.m.
[Amended 7-14-2009 by L.L. No. 18-2009]
(9) A beach fire must be fully and completely extinguished with water. No burning, smoldering, smoking, hot embers or debris shall be left on the beach. No beach fire shall be buried with sand.
(10) All fire debris must be removed and disposed of properly and the site must be restored to its natural condition at the conclusion of the night.

SH
§ 164-5. Permits.
[Amended 11-12-2002 by L.L. No. 47-2002]
A. A permit must be obtained from the Fire Marshal to conduct any of the following operations or to store, handle or use materials that are considered to present an extra or unusual fire hazard to life or property, as follows:
(1) Bonfires. All fires conducted outside of a building, except fires kindled for the instruction of personnel in the methods of fighting fires or small fires kindled in or upon the ground or in a barbecue pit, exterior fireplace, cookout device or other similar out-of-doors eating or cooking device.
§ 164-6.5. Penalties for offenses.
A. It shall be unlawful for any person to violate this article, to permit or maintain such violation, to refuse to obey any provision thereof or to fail or refuse to comply with any such provision or regulation except as variation may be allowed by the Fire Marshal. Proof of such unlawful act or failure shall be deemed prima facie evidence that such act is that of the owner or other person in control of the premises. Prosecution or lack thereof of either the owner, occupant or the person in charge shall not be deemed to relieve any of the others.
B. For any and every violation of the provisions of this article, which shall include the failure, refusal or neglect to comply with an order issued by the Fire Marshal, the owner, occupant, general agent, contractor, lessee, tenant or person in charge of an entire building, structure or premises where such violation has been committed or shall exist and the owner, occupant, general agent, lessee, tenant or person in charge of any part of a building, structure or premises in which part of such violation has been committed or shall exist and any other person who knowingly commits, takes part or assists in any such violation or who maintains any buildings, structures or premises in which any such violation shall exist shall be guilty of a violation and, upon conviction thereof, shall be punishable by a fine not exceeding $250 for the first offense, $500 for the second offense and $1,000 for the third and subsequent offenses or imprisonment for a period not to exceed 15 days, or both.