(Version of this post with links to the USC Ski & Snowboard Team, HMC “skiing SoCal” blog, and Stanford Ski Team was “flagged for moderation”… so feel free to search these up for yourself.)
It seems to me that you risk ruling out perfectly good options with the rigid double-major filter. The important thing for applying to graduate school is the coursework you’ve done, not whether your school awards you a single or double degree for it.
At any rate, USC is a particularly good place for making double majors happen, and they have many combinations of bio, chem, and physics. (Biochemistry, Biophysics, Chemical Biology, Chemical Nanoscience… plus all of the single-discipline majors and related engineering fields.) It’s bigger than you have in mind but more personalized than a similarly sized public U. And hits your internship and social life benchmarks.
Harvey Mudd is the right size if you take the whole Consortium into account. Their rigorous core curriculum already covers a ton of Bio-Chem-Physics. They have Bio+Chem and Physics majors, and Engineering, and an IPS: Individual Program of Studies major that can be used to combine fields if a formal double-major isn’t possible. (Which it might be, but we’ve come to the edge of my knowledge on that.) Social scene is active but has its own vibe/character which you might or might not love.
And obviously you could get what you’re looking for at Stanford if you’re a very competitive applicant.