The proposal is the latest example of local governments taking the lead on climate policy as the Trump administration pulls back. But it also reflects the dilemma that global warming represents for New York and other fast-growing coastal cities: Even as seas rise and storms intensify, so does the demand for building along the water.

On Governors Island, whose location in New York Harbor makes it particularly exposed to flooding and storm surge, that tension is part of the point, according to Michael Samuelian, who until June was head of the trust that runs the island.

“Being an island in the middle of a harbor — there’s no better place to put the heart of climate adaptation and education,” Mr. Samuelian said. He said Governors Island, which is less than a mile from Wall Street, should become a “visible representation of what these issues we’re going to be confronting are.”

The city has asked outside consultants to come up with specifics about what that might look like, as well as a “pitch deck” the city could use to sell the idea to foundations, universities or other possible partners. New York wants that work finished within six weeks, according to the document, so that it can solicit bids from developers by the end of next year.