Which wives of former US presidents were in your opinion, the most influential?

Eleanor Roosevelt. She was a great humanitarian in her own right and positively influenced the course of the country during the Depression. There are others, but she stands head and shoulders above the crowd.

Nancy Reagan. Ronnie was often lights out to the world, and she took up the slack.

After Wilson had his stroke his wife was the president.

Eleanor Roosevelt, Abigail Adams, Edith Wilson, and Lou Harding. Also Hilary Clinton.

Eleanor Roosevelt (for the better), Hillary Clinton (for the worse), Nancy Reagan (for the much worse) have already been cited.
I would add Jackie Kennedy. She added class and style to a Presidency that occasionally faltered. America became obsessed with her, and followed her life after Jack with a microscope.

Jackie was a girl, who was mistreated by her husband, and had no meaningful influence except upon fads and fashion. She grew into a great lady in middle age.

Jackie’s influence was not on policy, but on perception, and she helped JFK remarkably here.

Nancy Reagan’s astrologer. Seriously, Eleanor Roosevelt.

Reaganomics came directly from Nancy. Even her astrologer didn’t see it coming.

I take your word for it ;-)

My astrologer told me so!