Carnegie Mellon University
Harvey Mudd College
Rensselaer Polytechnic Institute
Worcester Polytechnic Institute
Keep in mind, many top engineering, mathematics and computer science departments are not in “tech” schools. Check out the following:
Brown University
Columbia University
Cornell University
Johns Hopkins University
Northwestern University
Princeton University
Rice University
Stanford University
University of California-Berkeley
University of California-Los Angeles
University of California-San Diego
University of California-Santa Barbara
University of Chicago (they don’t offer Engineering, but they are excellent in Mathematics and Science)
University of Illinois-Urbana Champaign
University of Maryland-College Park
University of Michigan-Ann Arbor
University of Pennsylvania
University of Rochester
University of Texas-Austin
University of Wisconsin-Madison
Also keep in mind that just because a “technical institute” focuses mainly in the STEM fields does not exempt you from having to take non-STEM classes. In fact, you would probably have to take fewer non-science classes at Brown than you would at Caltech or MIT.