Are there any Ivies or similar level peer schools where legacy doesn’t play a role in admissions?
JHU, MIT
All of the Ivies consider legacy, to an extent. Off of the top of my head, JHU, CalTech (which makes sense lol,) MIT, and UC Berkeley/LA (though this is debatable given the recent scandals.) Most schools state on their Admissions websites if they consider legacy (it may be hidden in the FAQ section, or on their Alumni section,) and a google search should bring up relevant info.
Not having legacy at a school shouldn’t stop you from applying, as I didn’t have it and was still admitted to some of the schools that consider it. Legacy status tends to mean more for applicants who are applying early, and is much less of a factor between similar applicants RD, and it would be impossible for schools to justify why their classes are virtually all legacy students. IMO, if you meet the score ranges and have decent ECs (read past CC threads for examples, though keep in mind that CC’s a self-selecting population,) apply widely (safeties, matches, and reaches,) and hope for the best! 
Hope that helps!
Penn seems to weigh legacy more for ED. From their site: “We appreciate that attending Penn is a tradition for many families, so an applicant’s affiliation with Penn, either by being a child or grandchild of alumni, is given the most consideration through Early Decision.” https://admissions.upenn.edu/admissions-and-financial-aid/preparing-for-admission/freshman-admission/early-decision-and-regular
Cornell also weighs legacy in ED. Admissions has said to alumni that it isn’t a bump at all in RD.
The scandals were in the context of large donors influencing admission in unauthorized ways in violation of existing policy against development admissions (Regents Policy 2202), not ordinary legacy situations (which are also not supposed to be considered).
This adds some major respect points for MIT, CalTech, Johns Hopkins. I guess with their high academic standards, they really aren’t the ideal destinations for applicants using backdoors.