A decent physics major degree program should include the following junior and senior level course offerings:
quantum mechanics (typically two semesters)
electromagnetism (typically two semesters)
analytic mechanics
statistical and thermal physics
advanced physics lab
physics electives, possibly including astronomy
math courses like real analysis, complex analysis, and abstract algebra
A quick check of course catalogs should tell you whether a school is suitable for majoring in physics at. Be sure to check schedules to determine the frequency of offering; courses offered "occasionally" or once every two years may be inconvenient to build a major out of.
Some expensive schools do offer decent financial aid; check the net price calculators. (Harvard and Yale are known for good need-based financial aid, though getting in is the hard part.)
If you have high test scores, you may want to check to see if any of these schools have worthwhile physics offerings:
Automatic Full Tuition / Full Ride Scholarships
If you make National Merit Finalist, check these schools as well:
NMF Scholarships: An Updated Compilation
And if you can afford about $35,000 per year, check the physics offerings at the schools in the following list (or go to the link to the ed.gov site and reset the parameters as desired, including changing the test score screens and adding a physics major screen):
Less expensive (list price) less obvious schools that attract "good" students 
