It's actually a huge misconception that Stanford Hospital does not get a similar patient base compared with academic hospitals located in cities. Keep in mind that although Stanford is located in a suburb, it is in the middle of the VERY densely populated South Bay (I think the population of just the South Bay alone is something like >1.5 million people). In addition, there have been a number of recent hospital closures in the community, including San Jose Medical Center, so all of those patients are now coming to SUH and Santa Clara Valley (both of which are major teaching hospitals for Stanford students.) SUH is busting at it's seams with patients, which is good for students, but has been causing problems with the residency programs (they're trying to figure out how to deal with the increased workload on the residents). So if you're concerned about patient volume, that certainly is not an issue.
Now as far as the diversity of cases go, I think it's similar to what you would see at most major academic medical centers. I'm currently doing my residency at an academic hospital in a metropolitan city, and I actually haven't noticed much of a difference in the types of patients/cases that I see compared with SUH. About 50% of patients seen at SUH are referrals from other institutions. SUH is a major referral center serving the South Bay, central California coast, the central valley (including Fresno and Modesto), and Nevada. The referral base not only adds to the diversity of cases seen, but also to the diversity of your patients. For example, the patients referred from the central valley are largely Hispanic, and are typically farmers (I have even taken care of real-life cowboys while I was there!). SUH also gets referrals from other areas, including Hawaii, Arizona, Oregon, and even the LA area. The referral base is really a gold mine for students to be able to see a ton of incredibly rare diseases and highly-advanced procedures/surgeries.
As far as the non-referral patient base, it's really about the same as most centers. You don't see nearly as many homeless patients as, say, Moffett Hospital at UCSF, but if you want to see homeless patients, you can do all of your rotations at Santa Clara Valley med center, which is the county hospital serving the city of San Jose. You will, however, see patients with HIV, as there is an HIV clinic affiliated with SUH (the hospital I'm currently at treats almost NO HIV+ patients in comparison!) There are some private patients as well as a number of local patients on Medical (CA's Medicaid), which give you a number of bread-and-butter cases to see.
If seeing the rare zebras isn't your thing, you can choose to do more of your rotations at the other affiliated medical centers. In fact, by the time you graduate from Stanford Med, you will have had to rotate through all 5 hospitals so that you get more of a variety of patients as well as seeing what different medical systems are like.
To briefly summarize the different hospitals you'll be at: SUH and Packard Children's are the two academic hospitals you'll rotate through. Packard has a similar patient base and referral pattern as SUH. Santa Clara Valley Medical Center is the county hospital for San Jose with it's own IM residency program, but the Stanford residents from all the specialties rotate down there as well. You will see the typical bread-and-butter cases, lots of uninsured patients, lots of both legal and illegal immigrants, tons of undiagnosed disease waiting for your diagnoses. Kaiser Santa Clara is the HMO hospital you'll rotate through - mostly middle-working-class patients with bread and butter problems - interesting to see how an HMO system works. Finally there's the Palo Alto VA hospital - VERY closely affiliated with SUH - the attendings at the PAVA are Stanford faculty, and all the Stanford residents and fellows spend a hefty amount of time there. The PAVA is the flagship VA hospital for the West Coast. You see a ton of typical vet problems, including out-of-control diabetes, heart disease, vascular disease, liver disease, and PTSD. But the PAVA is also a referral hospital for other VA's, so you will often some of the most severe presentations of these diseases.
So those are the hospitals. The nice thing about the mix is that they complement each other very well. Whatever one hospital may be lacking, you can get at another affiliated hospital.
And as a last note - to tell you the truth, I was a little concerned before I started at this other academic hospital for my residency. I started to buy in to the rumors that Stanford Med does not offer as good clinical training as other med schools, so was worried that I might have to do some catch-up. I was pleasantly surprised when I started. I found that I had just as good clinical training as my residency classmates, and compared to many I felt like I was more prepared.
Sorry about such a long post! I hope that helps!
Oh - and do try to go to the revisit weekend - it's a great weekend organized by the students, and will help to answer many of your concerns.
Let me know of any other questions.
The clinical training really concerns me, though. 
