I recently visited Universty of Illinois, Northwestern and Purdue. I absolutely loved Northwestern and I did not like Illinois at all. I wanted to reconsider the schools I am looking at and I wanted to look at schools similar to Northwestern. Price is not an issue, but I want schools with similar size, campus, and with a good engineering program.
Penn, Princeton, UIUC, Vanderbilt and Rice were on my son’s list. Iowa State, Purdue, UIUC and Rose Hulman were on my daughter’s list - and both chose NU for engineering. Iowa State would be the largest, and Rose Hulman the smallest, and IMO, Penn, Vanderbilt and Rice are NU peers. Good luck!
Also Case Western and Duke.
Look into Tufts, UNC Chapel Hill, Cornell, Penn, and Duke.
Your list won’t be that long if you are looking at similar size. Campuses tend to be much larger or smaller than NU.