I actually disagree with the above posts which state that Hopkins provides superior clinical training. I'm perhaps somewhat biased, as well as a bit better informed, than the above posters as I am a current Stanford student who entered clinical clerkships this year. I've gone through many of my core rotations (med, surg - not yet peds) and I can state that the clinical training is excellent.
Stanford Hospital, like Johns Hopkins Hospital, is a tertiary care center which means that it gets many transfers and referrals from area hospitals for complicated patients. It also serves as the primary care hospital for disadvantaged patients from around area including East Palo Alto, Redwood City, and much of the East Bay. In addition to Stanford Hospital, students rotate through the Palo Alto VA Med Center (PAVAMC), Kaiser Santa Clara, and the Santa Clara Valley Medical Center (SCVMC). All core rotations require students to be at multiple sites which provides a very diverse clinical experience. You'll see standard HMO-type patients at Kaiser SC and get a sense of how an HMO functions. The PAVAMC, although everyone says it about their own VA, is possibly the country's top VA. It's a great hospital and is an impressive research center in its own right. And finally, perhaps the best part of the training process, is SCVMC (also called The Valley). The Valley is a county hospital that serves disadvantaged and uninsured patients in San Jose and the South Bay. It's a large county hospital (for comparison, it's twice the size of San Francisco General and slightly larger than Cook County Hospital) - it's a great place and, like county hospitals everywhere, is very hectic and provides students with lots of opportunities. The Bay Area is possibly the most ethnically diverse area in the country and students have a lot of exposure to a variety of immigrant communities with varying levels of prior healthcare. I haven't done Peds yet so I can't talk as much about Packard Hospital and the peds training.
I think there is an East Coast bias against some of the west coast programs and there are long-standing attitudes that don't have a lot of basis in fact. It's hard as a pre-med to sort through this stuff because these things get passed around like the gospel truth and they ultimately don't mean much. On my clinical rotations, I've met current residents who went to medical school at Stanford and Johns Hopkins and I can't tell the difference between them in their abilities, etc. - I just know they are both farther along them I am and are both very good!!
In any case, you'll have lots of opportunities at both places and I'm sure you'll be able to accomplish whatever you want coming from either place. Good luck!
I used to post on these boards all the time as a pre-med and now I've just come back (under a new guise!) as I get ready to start the residency application process. Thought I'd check out the pre-med boards and saw people going through the same thought process I had a few years back (mine was HMS vs. Stanford and I'm glad I made the decision I did). Again, good luck!