NewYorkology, an online New York travel guide, has a great list of New York City museum, park or zoo with free or pay-as-you wish hours. That’s in addition to the museums that are always free or operate under a suggested-donation policy.

Mondays
Museum at Eldridge Street – Free tours every half hour from 10 a.m. to noon (normally $10)
Yeshiva University Museum – Free 5 to 8 p.m. (normally $8)

Tuesdays
Brooklyn Botanic Garden – Free all day (normally $8)
Museum of American Finance – Free 10 to 11 a.m. (normally $8)
China Institute Gallery* – Free 6 to 8 p.m. (normally $7)
May, June, September and October Wave Hill – Free 9 a.m. to noon (normally $8)
Off-peak months: July & August Wave Hill – Free all day (normally $8)
Morgan Library & Museum – Free access to the McKim rooms (Mr. Morgan’s library and study) from 3 to 5 p.m. (full museum access $12)

Wednesdays
Bronx Zoo – Admission by pay-what-you-wish donation all day (normally $15)
Museum of Jewish Heritage – A Living Memorial to the Holocaust– Free 4 to 8 p.m. (normally $12)
Staten Island Zoo – Free 2 to 4:45 p.m. (normally $8)
Museum of American Finance – Free 10 to 11 a.m. (normally $8)
Van Cortlandt House Museum – Free all day, 10 a.m. to 3 p.m. (normally $5)
Yeshiva University Museum – Free 5 to 8 p.m. (Normally $8)
NY Botanical Garden – Free grounds access all day, but “This does NOT include admission to the Enid A. Haupt Conservatory, Everett Children’s Adventure Garden, Rock and Native Plant Gardens (April–October), or Tram Tour” (grounds-only access normally $6)
Queens Botanical Garden – Free admission from 3 to 6 p.m. (normally $4)

Thursdays
Museum of American Finance – Free 10 to 11 a.m. (normally $8)
China Institute Gallery* – Free 6 to 8 p.m. (normally $7)
Museum of Arts & Design – Pay-what-you-wish 6 to 9 p.m. (normally $15)
New Museum – Free 7 to 9 p.m. (normally $12)
Museum of Chinese in America – Free all day, 11 a.m. to 9 p.m. (normally $7)

Fridays
Museum of Modern Art – Free 4 to 8 p.m. (normally $20)
Whitney Museum of American Art – Pay-what-you-wish 6 to 9 p.m. (normally $18)
Morgan Library & Museum – Free 7 to 9 p.m. (normally $12)
New York Aquarium – Pay-what-you-wish 3 p.m. until closing (normally $13)
International Center of Photography – Voluntary contribution admission 5 to 8 p.m. (normally $12)
Folk Art Museum – Free 5:30 to 7:30 p.m. (normally $12)
September through June only: NY Hall of Science – Free 2 to 5 p.m. (normally $11)
Rubin Museum of Art – Free 7 to 10 p.m. (normally $10)
Suspended July 4 through Labor Day: Asia Society – Free 6 to 9 p.m. (normally $10)
Museum of American Finance – Free 10 to 11 a.m. (normally $8)
Yeshiva University Museum – Free 11 a.m. to 2:30 p.m. (normally $8)
Bronx Museum – Free 11 a.m. to 8 p.m. (normally $5 suggested)
First Fridays only Neue Galerie – Free from 6 to 8 p.m. (normally $15)
First Fridays only: The Noguchi Museum – Pay-what-you-wish on the first Friday of each month, all day, 10 a.m. to 5 p.m. (normally $10)
First Fridays only: Children’s Museum of Manhattan – Free the first Friday of each month 5 to 8 p.m. (normally $10)
Third Fridays only: South Street Seaport Museum – Free admission from 5 to 9 p.m. but only on the third Friday of each month, sometimes with free harbor sails (museum admission normally $10)

Saturdays
Guggenheim – Pay-what-you-wish 5:45 to 7:45 p.m. (normally $18)
Jewish Museum – Free all day, from 11 a.m. to 5:45 p.m. (normally $12)
Brooklyn Botanic Garden – Free 10 a.m. to noon (normally $8)
Museum of American Finance – Free 10 to 11 a.m. (normally $8)
Wave Hill – Free 9 a.m. to noon (normally $8)
NY Botanical Garden – Free grounds access from 10 a.m. to noon, but “This does NOT include admission to the Enid A. Haupt Conservatory, Everett Children’s Adventure Garden, Rock and Native Plant Gardens (April–October), or Tram Tour” (grounds-only access normally $6)
First Saturdays only: Brooklyn Museum – Free admission and programs from 5 to 11 p.m. on the first Saturday of most months (normally a suggested $10)
Third Saturdays only: El Museo del Barrio – Free 11 a.m. to 8:30 p.m. (normally a suggested $6)

Sundays
Frick Collection – Pay-what-you-wish 11 a.m. to 1 p.m. (normally $18)
Studio Museum in Harlem – Free noon to 6 p.m. (normally $7 recommended)
Queens Botanical Garden – Free admission from 4 to 6 p.m. (normally $4)
Morgan Library & Museum – Free access to the McKim rooms (Mr. Morgan’s library and study) from 4 to 6 p.m. (full museum access $12)
September through June onlyNY Hall of Science – Free 10 to 11 a.m. (normally $11)