Every city has a secret garden. New York has several - those exquisite small museums housed in former homes or privately donated buildings, with precise, unusual collections, meticulously researched and smartly shown. Each of these museums has a special ambiance, a distinctive character, often in keeping with that of the donor.
My favorite is the Frick at 1 East 70th Street, the low, rambling house of white limestone built in the style of an 18th-century French country house. Rooms are decorated with French and English furniture of the same period. It was the home of Henry Clay Frick, who made a fortune in steel and coal.
He collected furniture, sculpture, porcelains, paintings, and books, most of them from the same period. They are displayed in a natural way, like loved objects in a private home, and they must be viewed that way. The Frick is a place to come home to, again and again, to the Vermeers, the Fragonards, the Rembrandts, and perhaps, to the one special painting each of us loves best. Mine is the moody, thoughtful young woman in gray-blue silk by Ingre, ''Comtesse d'Haussonville,'' which hangs in the courtyard hall.
What makes the Frick so special is this interior courtyard with plants and flowers around a long, rectangular pool. Acoustics here are excellent, and one day not long ago I came upon a marvelous brass quintet playing Handel here; concerts are given throughout the year (Tuesday-Saturday, 10-6; Sunday, 1-6; 288 -0700).
The Pierpont Morgan Library, 29 East 36th Street, is another magnificent small building, built originally as a private library in the style of a Renaissance palace. Like the Frick, it is a pleasure just to walk through. Sit down in the interior marble rotunda and look at the colors: green-toned columns, walls veined with mauve, topaz, blue, and violet. There are paintings, sculpture , and gold and enameled objects of the ancient, medieval, and Renaissance periods.
The two original library rooms have high, carved ceilings, wall-size tapestries, rare Oriental rugs, and antique furniture. Rare books gleam behind glass and fretwork panels. Behind them, a secret door leads to an interior chamber. (The guard might show you how it works.)
The Morgan is a research library, but there are regularly changing displays of old books, manuscripts, letters, drawings, and early music (Tuesday-Saturday, 10:30-5; Sunday, 1-5; 685-0008).
The Cooper-Hewitt Museum at 2 East 91st Street is one of 10 museums in what is known as the ''Museum Mile,'' from 82nd Street to 104th Street on the East Side. The house, of solid stone and brick like Georgian homes in England, was built in 1898 with 64 rooms for Andrew Carnegie, his wife and daughter and 19 servants. Heavy oak halls, stairway, and ceilings contrast with delicate architectural details in smaller rooms, and green plants in the conservatory. A lovely large garden is open to the public.
Cooper-Hewitt is part of the Smithsonian Institution, and is the only museum in this country devoted to design. Its imaginative shows are focused on a single enterprise, like the current one on ''Writing and Reading'' (until Jan. 3 ), and one on puppets and puppetry (Dec. 15-Feb. 21). (Tuesday, 10-9; Wednesday-Saturday, 10-5; Sunday, 12-5; 860-6868)
Very different in tone is the small, serene town house at 1083 Fifth Avenue which is now the home of the National Academy of Design, the oldest art gallery and art school in New York City, perhaps in the country, dating back to 1825. The house is narrow, with cool, cream-colored marble walls and stairs, and a bronze statue of Diana poised at the bottom of a circular staircase like an exclamation point.