@intparent @firstsax I think we can back up what firstsax says with a quick back-of-envelope calculation.
Using https://www.caltech.edu/content/caltech-glance and http://web.mit.edu/facts/faqs.html
I see (hopefully am grabbing comparable faculty numbers):
MIT 11,000 total students including 6800 grad students to 1036 faculty.
Caltech: 2200 total students including 1200 grad students to 300 faculty.
So there are almost as many grad students to faculty at MIT as there are total students to faculty at Caltech. The total research positions available for undergrads is presumable net the grad students, so I think Caltech is pretty hard to beat.
Though clearly both are great. And at MIT you can find additional research opportunities at nearby places like Harvard as well, though they would be less convenient.