It's amazing what comes up. A lot depends on your deposit. If you can swing a total cost of ~$750-850k home price then you have a LOT of options in the East Bay.

There are some really nice places that show up in Rockridge that are reasonable and if you're ok with a little less nice of an area the NoBe area is good too. In Oakland you can do surprisingly well near Highway 13 in the foothills or nearish Mills College.

If you don't mind the commute (I would) then Pleasanton is affordable (just) for large single-family homes, but it's a long ass commute.

There's a ton in the Fremont/Hayward area if you're doing a South Bay commute tho, and that opens up Pleasanton a bit more too.

If you're already driving to work then look to neighborhoods nowhere near BART as reasonable proximity to that can add a 1.5-2x multiplier to the price.