The New-York Historical Society has long seemed like a remote fortress on Central Park West because of the stately but insular architecture of its stone building and a certain bumpiness in its public relations.

A sale of part of its collection in the 1990s, a shift to a more national focus a decade later, and plans, since abandoned, to build a tower and five-story annex, have at one point or another put the museum at odds with preservationists, city historians or neighborhood groups.

But with a $65 million renovation that is nearing completion, the museum is reaching out to the public with a redesign that tries to be welcoming and to communicate the treasures that lie within a building originally designed by architects who specialized in banks. The society will announce additional details of the changes on Tuesday.

“It was designed as a vault, to keep treasures safe, not to invite the public to enjoy them,” said Louise Mirrer, the society’s president and chief executive, during a recent tour of the work. “We feel very differently about the public. There’s really no point in having these extraordinary collections if people can’t learn something from them.”...