Avoid West Oakland (especially near the harbor, avoid anything west of Mandela Parkway or even west of I-980) which is the most dangerous area, as well as Fruitvale and south (eg: San Leandro), and Richmond in the East Bay (the Richmond district in SF is very safe). Alameda island is quite safe, as well as Chinatown and Broadway near the BART stations and Lake Merrit. Berkeley, the Oakland hills and Piedmont area are also safe. But I would still avoid walking around at night in downtown Oakland by myself after 8PM.

In SF, I would avoid the Tenderloin, parts of SOMA from 6th Ave and higher, Mission district below 20th Ave, Excelsior, and Hunter's Point as well as the Bayview neighborhoods. Avoid East Palo Alto in south bay (the rest of Palo Alto is quite safe).

For short-term housing, this could be a good option if your budget is ~$1000/month: Berkeley is generally quite safe https://och.berkeley.edu/housing-secondary/price-under+1100/...

There is modestly more property crime in Oakland, and slightly more violent crime in certain parts of Oakland, but really, if you’re not coming back at 2AM (which wouldn’t work anyway, BART stops about midnight) it’s really not a problem for tourists.