It would be hard to beat Jackie Kennedy's extreme popularity during the JFK administration. The JFK administration itself was relatively transformative with respect to the evolution of American society and cultural norms and Jackie certainly played a role in that. Jackie oversaw an extensive renovation of the interior decoration of the White House, which had languished under years of poor maintenance up until a major reconstruction work in the Truman administration (which completely gutted and reworked the interior) and afterward didn't get much attention in terms of interior decoration (being filled with many ordinary home goods). Jackie "classed up the place" with carefully selected decor of often historic significance.

She also spurred a transformation of the White House from essentially the personal residence of whoever was president (who treated it as such, and took whatever they wanted from the residence when they left office) to more of a living museum with items of historical significance staying with the White House even through changes of administration. She helped drive congress to establish that White House furnishings were the property of the Smithsonian, and she helped create a lot of the administerial components which have looked after the White House as a setting with historical value.

In early 1962 she went on television to provide a tour of the renovated White House and enthralled the nation with her work and herself. 56 million viewers in the US watched the tour and she even won a special Emmy award for it. Jackie's ongoing advocacy for the preservation of history as well as the arts and diplomacy made her a well regarded household name. Jackie's trend setting fashion sense and social skills made her extremely popular in elite social circles, across the nation, and across the world. No first lady before or since has been as active, influential, or popular.

Runners up: Eleanor Roosevelt, Abigail Adams, Dolley Madison.

As to the low point of first ladies, keeping in mind the restriction of this sub-reddit to avoid anything within the last 20 years (let alone the last 2, ahem), well, this is actually a somewhat challenging question. Many of the first ladies who were inactive or unliked within the elite Washington, DC social circles did not typically have a very high profile at a national public level. And in the TV and mass communication era even the most "controversial" first ladies (such as Nancy Reagan and Hillary Clinton) never saw disapproval levels dip as low as any of the presidents did. But if I had to pick I'd probably go with Jane Pierce, who disapproved of her husband (Franklin Pierce) becoming president and spent most of his administration avoiding DC high society entirely (often pawning the job off on her aunt). She had 3 sons, the first lived 2 days, the second 4 years, and the third 12 years, dying in a train accident only 2 months before the the inauguration. She spent the first two years of Pierce's administration in a depressive funk, more or less confining herself to the 2nd floor of the White House. She eventually began to sporadically serve as hostess for White House functions. While her reactions to tragedy are understandable Washington society at the time still felt spurned.