Chance Me: Caltech, MIT, Northwestern, Duke, Tufts, etc.

I agree with @theloniusmonk 's comments… eliminate a few and consider ED somewhere. You might want to consider Rice and/or Wash U in St. Louis. Both have great engineering programs with strong connections to their medical communities.

Engineering at Georgetown is their 3-2 program with Columbia which would be a very different experience than a traditional engineering program.