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Are you commuting to San Francisco, or somewhere else? If it's to SF, I'd take Fairfax off the list (except *maybe* if your commute is very near the GG Bridge).
I'd look in Albany near El Cerrito Plaza BART station; that's probably the best bang for the buck. There's a lot of rental housing and a lot of smaller homes and condos, which would be fine for a family of two. (Albany is only affordable---relatively!---because it's built out and the houses tend to be small bungalows.) You're close enough to Oakland and Berkeley to get to things like capoeira fairly easily. It's not the world's most diverse city, but definitely moreso than Fairfax (which is 90%+ white).
The challenge with Oakland is that the areas with good schools have relatively little rental housing available, and the homes are typically bigger (good schools = higher income neighborhoods = higher rents and large more expensive homes). They also tend to be less transit-accessible, except for the Transbay bus to the Financial District. Rockridge is the exception (BART station + great elementary schools) but rents are pretty high there.
The other place that comes to mind is Alameda, which could be worth considering depending on where you're commuting to.
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