Ever since Ted Conklin’s 1972 reinvention of the American Hotel, built in 1846, it has been writing a new chapter of its long history. He has established a place where plumbers and carpenters are comfortable at the bar with literary heavyweights. With Empire and early Victorian furnishings, an anteroom and four small dining rooms have an intimate feel, and the service and ambience are both traditional and top notch. The serious menu is grounded in classical French cooking with some Italian or Asian additions. While some prices may top other South Fork restaurants — a $150 seafood platter with caviar, for example — the restaurant has nicely prepared simple entrees at prices that are standard. Eggs Benedict and French toast are served on Saturdays and Sundays. The wine cellar, reputed to be the most distinguished on Long Island, has about 1,700 selections, ranging from below $35 to $5,000 a bottle. The hotel has eight suites available upstairs.