Two venerable New York museums — The Metropolitan Museum of Art and The Museum of Natural History — have a suggested ticket price of $20, or more. Admission is actually by donation so, if you are on a tight budget, you can pay what you wish.
This means if you can afford only one dollar, it will be enough to get you through the door. Cashiers are fine with this as many New Yorkers who know this policy pay according to their means. No one will bat an eye or say a word.
This makes visiting with a partner, friend or family far more affordable, and frees up some money for when you visit fixed price museums like The Neue Gallerie (check the article), The Frick (at 71st and Fifth Avenue, just downtown from the Met) or The New York Historical Society, across the street from the Natural History Museum on the West Side of Central Park.
By the way, the Gem Gallery at the Natural History Museum has just closed for a substantial facelift. It was where you can see the Star of India, one of the world’s largest sapphires. Their collection is mind blowing. I go there to be awed and amazed, in a quiet setting. Alas, plans call for a full brightening and ease of access—no more quiet setting.