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.
Whereas I live in Oakland and door to door it’s about 45mins if I time it right.
So I’m not sure what your objection is. Working in a big city (be it SF, NYC, or London) means you’ll have commute time.
Now it'll likely be a condo, not a single-family home (that'll be more, or further way, or not as nice) but it's doable for sure. Not in SF, but just outside (Oakland, Fremont, Daly City, etc)
What you can get will depend on what you can wrangle as a deposit but there are plenty of options if you can get 10% down.
Source: it’s what I did recently and I pay less than that for a 1300sq ft place in Oakland