Some other schools which are equally strong in the profile you're looking at, and which may have slightly better odds in terms of acceptances--
Harvey Mudd
University of Washington
Maryland, as Cranberry mentions-- there is a university honors college at Maryland, I know.
Check out the possibilities of some of the honors colleges housed within larger public research unis-- they may have those low acceptance rates and VERY high average stats, but your odds are quite simply better there because they lack the inundation that a place like MIT or Princeton is going to get.
But be aware that most honors programs are housed in the social sciences or humanities-- so choose carefully and take a look at what the curriculum has to offer.
We did that and DD has been quite happy with her choice-- most math classes up to 400 level (and even some of those) are offered as a small honors-only section, she gets priority registration, and there are a lot of other small perks to being in the program.
I'd look hard at some of the 'sleeper' tech schools, too, if STEM and particularly engineering is a possibility. RPI, Lehigh, etc.
Brandeis?
Virginia, depending upon interests?
Cornell?
We looked at a great book for finding more student-interest-specific matches in colleges when DD was looking, 3y ago. Can't remember the name of the darned thing, though-- sorry.
Also be aware that age probably isn't AS big a factor as you're thinking, here. Those are schools where the majority of highly qualified applicants get rejected, too.
It is quite literally the case that nobody can really count on getting into MIT or a school like Caltech, Harvard, or Stanford. Nobody. The rejection rate for those schools is in the high ninety percent range. Probably only about one in four or five of those rejected really couldn't manage being a student at the institution.... so.
Rmember, too---
where you go is not who you'll be.
I realize that it's very easy to mourn something that you might have really, really wanted for your child, but the healthy thing here is to keep the adult perspective, which understands that life is a LOT longer than college. You can get an excellent-- even transformative-- education at almost any school.
