From the street, the brick tenement on Avenue C looked like any other building. But inside on Saturday afternoon, about 30 people gathered to look at a storefront space covered with graffiti and murals. 

“This is C-Squat,” Laurie Mittelmann explained to one of the spectators, “soon to be home to the Museum of Reclaimed Urban Space.”

That museum, Ms. Mittelmann said, was being established to, among other things, tell the story of how activists in the East Village took over abandoned properties and over the years transformed them into permanent housing or community gardens.

She said that she came up with the idea for the museum with Bill DiPaola, the executive director of an environmental group, Time’s Up, whose members participated in demonstrations to preserve community gardens and squats....