They are located sort of near each other but in very different communities. Both have a very high cost of living. Berkeley is more urban and gritty, with lots of diverse people taking public transportation. There is more homelessness in Berkeley and a long history of being very liberal with a culture of being "counter-culture." You can take BART from downtown Berkeley into San Francisco or other nearby cities. But much of the campus and community is still very beautiful. Stanford is more like a pristine resort with palm trees and people driving cars instead of the bus. The area feels more suburban and spread out. The Stanford students are probably diverse, but the nearby community is overall more wealthy and less diverse. But you have access to the traditional part of Silicon Valley from Stanford, though this means less now since so many of those jobs are now also in San Francisco and spread into the entire Bay Area.

I hope that helps give some overall impressions. You will find amazing smart people on both campuses.