I, like @Shelby_Balik, originally thought @thumper1 was thinking of the Wheaton in IL (based on the mention of religious affiliation as a differentiating factor between Yale and Wheaton). For sure Norton, MA and New Haven, CT are different as are the financial resources of the schools, etc. But I don’t think either has a religious affiliation; Brown and Wheaton both have the open curriculum (but not Yale which I think has a pretty typical list of distribution requirements)? Wheaton no longer has the Connections Curriculum that @tsbna44 found mention of in an article…it was replaced several years ago with the open curriculum during the time when a Brown grad was the provost at Wheaton (MA).
@cag2, in terms of schools for the list that are easier admits (agree it would be helpful to know what your D loves about Yale (and Brown) to make better suggestions,) my D loved Brown (for its open curriculum, vibe/culture, location, size, etc.) and found lots to love (or at least very much like) about Beloit, Dickinson, Macalester, Denison, Oberlin, Bryn Mawr, Dickinson, Skidmore…She also loved a lot about some additional reachy schools (Pomona, Vassar, Smith, Wes, Wellesley, Grinnell, Carleton, etc.) In every case, there were things that weren’t the same at these other schools as Brown and tradeoffs to be grappled with (Grinnell Iowa is not particularly similar to Providence, RI; a suburb of LA is not a small New England city, long lists of distribution requirements are not the same as an open curriculum, etc.), but lots of research led her to feel really good about a lot of different options.
For the attributes that seemed most important to her during the application process, Vassar and Smith were maybe the ones that came closest to Brown overall, but in the end she chose neither Vassar nor Smith even though both were options. Maybe some of those schools would appeal to your D (though she’ll still need to decide whether to apply early to Yale). Two kids at my D’s small public high school got into Yale last year. Both had outstanding ECs. One applied REA and was deferred and then accepted. The other applied RD and was accepted. Both got into at least 4 or 5 single digit acceptance rate schools - their applications had the strong academics but also something unique outside the classroom.