The Fairfax Hotel at 2100 Massachusetts Ave. NW, operated by the Gore family since the mid-1930s, is being sold along with more than a dozen nearby Gore properties to Chicago industrialist John B. Coleman for more than $5 million.

Coleman, owner of the luxury-class Tremont and Whitehall Hotels in Chicago, said yesterday that he plans to redecorate the Fairfax substantially, probably in a Williamsburg theme. His associates said he intends to turn the 140-hotel into a facility catering to corporate executives and businessmen, much like his Chicago hotels.

The Fiarfax's restaurants, the Jockey Club - described by Holiday Magazine in 1962 as Washington's first elegant restaurant - and the Sea Catch, a four - star seafood establishment, were included in the sale and will remain essentially the same, Coleman said.

The hotel building is owned by Jamie Gore, wife of "Col." H. Grady Gore, one-time Maryland politician and retired millionaire realtor. Their four children - Louise, Republican candidate for Maryland gevernor in 1974; H. Grady Jr., Mary Gore Dean and James - share the ownership of the restaurants.

Gore family members are also selling town houses and other properties near the 21st Street and Massachusetts Avenue site of the hotel to Coleman.

Col. Gore, 82, and his family have been looking for a buyer for the hodings for several months, it was learned. The sales contract was signed Monday, but its details have not been disclosed.

The Fairfax, described by parties to the negotiations as in need of "substantial" amounts of work, includes 30 to 40 apartments in addition to its guest rooms.

Coleman, who owns paper, packaging and drug-related companies around the country in addition to his hotels and other real estate, said he has "no intention to expand the hotel at the present time."

His two Chicago hotels are older facilities that have been renovated with a European flair, featuring antiques, reproduction and touches such as Currier and Ives lithographs. The hotels' rate range upward from $44 a night.

The restaurant at the Tremont is run by the operators of New York's at 21 Club, but Coleman said no decision has been made about bringing that management to the Fairfax.

Louise Core opened the Jockey Club in 1960 after more than 20 years as part-owner of the Fairfax's beauty shop. Socially active, she staged parties there to promote the restaurant, deducting the cost from her own salary. Later, while U.S. ambassador to the United Nations Education, Scientific and Cultural Organization, she visited Paris' restaurants to plan the menu for the Sea Catch.

Coleman said he is eyeing the hotel investment possibilities in other cities but has no plans at the present. He leases the Whitehall to a London hotel firm.

Coleman would not say if Gore family members would remain with the fairfax in any capacity. The family was not available for comment yesterday.