Huge (good) question. First, some books I'd recommend.

Pach and Richardson's The Presidency of Dwight Eisenhower

Campbell Craig's Destroying the Village: Eisenhower and Thermonuclear War

Saki Dockrill's Eisenhower’s New-Look National Security Policy, 1953-1961

William M. McClenahan Jr., and William H. Becker.'s Eisenhower and the Cold War Economy

and (just one more, I promise)

The Statler and Johns edited The Eisenhower Administration, the Third World, and the Globalization of the Cold War

These are a fair range of the past 20+ years on Eisenhower's national security and foreign policy with some on the domestic - which I'm going to deal with in a bit. I could recommend a literal dissertation's worth of books, articles, and other sources, but these are simply some "good" sources for a grounding.

So, what did he do to that has been remembered positively? He spent a great deal of time and energy trying to restrain spending across the board, avoided a large-scale war, never caused the U.S. to be greatly embarrassed (Truman, Kennedy, Johnson, Nixon, et al. could not make such claims), and is generally remembered to have presided over a period of stability and prosperity both at home and abroad.

The issue with this, which is popping up more and more among historical works is that both domestically and in foreign policy, this remembrance is more myth than fact. I'm not a domestic expert, but the clearest example is race relations. While Eisenhower's presidency did see very minor advances on discrimination and segregation, it was not in any way spurred on by Eisenhower. The Little Rock crisis came about more because Eisenhower was enraged at Faubus than because he felt any sort of support for desegregation. One could also examine his dismal record as a party "leader" or other issues, but I'm far from an expert there.

In foreign policy, historians like Robert McMahon, James Meriwether, Kathryn Statler and others (full disclosure: once my dissertation is complete I'll be a more cantankerous member of this school of thought), have pointed out Eisenhower had a very problematic perspective on the "Third World" and other areas. I won't go far into his national security policy or his stance on nuclear weapons but to say they were problematic is polite and generous.

Eisenhower will, more and more, be remembered negatively for his treatment of and dealings with non-European states. In these areas, Eisenhower left a more unstable, arguably more dangerous world which in many ways created the foundation for the explosion in anti-American sentiment which began to plague American foreign relations as the Cold War went on and into today. This is not to argue Eisenhower was the first to take a patronising or antagonistic approach to the Third World, only that he made a conscious decision to continue, and in some cases escalate such treatment.

When I say this barely scratches the surface, I'm understating things grossly. Eisenhower continues to be remembered positively for a variety of reasons, and I'm in no way suggesting all or even most of them are myths or fabrication. Indeed, comparing Eisenhower's presidency warts and all to other modern examples, and he still comes out looking fairly good in most cases. My central criticism of the erroneous remembrance of Eisenhower is that while other presidents are criticised for their errors and for the problems they leave or cause for their successor, Eisenhower typically escapes such things. But, he left, and indeed caused a great deal of problems which (especially) Kennedy, but also Johnson, Nixon, and other presidents had to deal with.

His "Military-Industrial Complex" address is rather famous as him warning future presidents, but it's also fairly standard Eisenhower: Here's a problem I noticed, and a vague solution that's not in any way actionable. He did that sort of thing all the time, and then complained and blamed officials when nothing changed or happened. This is certainly not unique to Eisenhower, but again, it's something he rarely faces criticism or is remembered for which I think needs to and slowly might, become a part of the popular memory.

EDIT: I could go on, but I'm sure others have differing and valuable perspectives as well, and I was about to veer into a story about Eisenhower nearly attacking Indonesia with submarines, so I'll leave this as it is unless a larger discussion ensues. I hope this is helpful!