Are we talking graduate school? (Since you're asking about research).
If so, the short list of top programs is probably Johns Hopkins, Emory/Georgia Tech, UCSD, Duke, and then some of the usual suspects (MIT, Stanford, Berkeley, UMich, UWash, etc).
For undergrad I don't actually know, but it's probably a similar list. In particular, if you can get grad research experience as an undergrad, the strength of the graduate program actually might matter more anyways :P
But of course cost is an issue, so if you have an in-state program that isn't bad, then doing that and then a follow-up PhD (which is usually free) in a top school would be a good approach too.
Edit: looks like I was wrong, it's UCSD not UCLA that has the stronger biomed eng program