You consider Michigan an in between? Not as selective as the Ivys but much more selective than GT and Purdue.
I'm in the same position. My son has applied to a number of highly selective schools but says he's OK with RU as long as he gets in the Honors College.
Here's his list in order of preference: MIT, Stanford, Carnegie Mellon, Cornell, Columbia, Penn, UC Berkeley, Rutgers, UCLA. He is going to pursue Computer Science.
The first 3 on that list are next to impossible admits (less than 1 in 15), and many kids with perfect SAT scores and grades get rejected. Cornell, Columbia, Penn, and Berkeley are long shots too. And have heard UCLA Comp Sci admit rate is below 10%.
Thought that Michigan, Purdue, and Georgia Tech would be somewhere in the middle, but he wanted the Northeast or West Coast.
From many incidental discussions and reading the boards on College Confidential, there is more to admissions than perfect (or near perfect) SAT scores and grades. And while it used to be the case that doing a bunch of activities helped your resume, now colleges want applicants to demonstrate a passion and accomplishments in one area. They are also keen on community service. And the Ivies we visited as well as Stanford are committed to giving applicants who are first generation college students admission--which may mean an applicant with lower scores, grades, etc. may be chosen for admission over a "more qualified" applicant.