An Ivy League university. Distinguished law firms with Fortune 500 clients. The highest levels of government in the nation’s largest city.

As President Trump seeks to extract concessions from elite institutions and punish his perceived enemies, some of New York’s most powerful people are suddenly confronting excruciating decisions.

The hard choices they face seem almost to be pulled from the pages of a college ethics textbook: Fight back and put your institution and even your livelihood in jeopardy? Or yield and risk compromising foundational values and ideals?

Some have sued, or walked away from their jobs. Others have cut deals with the Trump administration, and faced ferocious criticism for what many see as capitulation.

Mr. Trump has sought financial agreements, fealty pledges and other concessions from all across the United States, and even from other countries. But his former hometown, New York City, is a prime target: It is a capital of industrial and cultural institutions — and of the elite liberal establishment that his presidency pits itself against.

The deal-cutting has come as a shock to some leaders.

“I have been surprised at the rush at times to assuage the White House from activity that has gone on from people who I just thought would display more courage,” said David Paterson, a former Democratic governor of New York.