I don’t know where you live right now, so it’s hard to contrast it to what you’re used to.
Berkeley and Oakland both have a lot of culture, but more often than not, living in Oakland also comes with the price of living in the murder capital of California, and the city with the 6th highest murder rate in the country. That crime does not really spread up to Berkeley, but it does spread somewhat into Emeryville (which is between Oakland and Berkeley, on the west side).
The south bay, in contrast, is more often than not a corporate park, strip mall (with few sidewalks and lots of large shopping centers), or a residential area. There is very little culture down in the south bay.
Oakland’s downtown area is nearly empty at night, and the street lights are too high, too dim, and too sparse, resulting in a very dark and creepy downtown area. It’s the sort of place you look at a few times and think “this is scary, and I want to leave”. The parts of Oakland that aren’t like this (like Jack London Square) feel contrived and corporate (large AMC cinema, lots of parking spaces, etc—it doesn’t feel like it is the natural progression of a city, and doesn’t feel like it has any history to speak of (although, I’m sure it does, knowing Oakland)).
Berkeley’s downtown, in contrast, is well lit, has numerous locations that are open late, is well populated, and is accessible. You will never have a shortage of nightlife and culture, if you want it. It’s all really close to campus as well, so you’ll definitely get to see it. Most importantly, the restaurants and stores are mostly independent, so you can feel good about giving them your business.