Hi Sandra,
I'm a professional property manager in Pleasanton, CA. I've owned rentals in the East Bay, as well as out of state in OH and TX. It's really hard to beat the long-term wealth building opportunity that the Bay Area offers. The East Bay offers great appreciation and a lower price than the South Bay or Peninsula. As previous responses have indicated, it's almost impossible to cashflow anywhere in the Bay Area without a substantial down payment. If you have a large down payment (or the ability to cover negative cashflow), the East Bay's appreciation and principal pay-down benefits have been historically very strong compared to other markets.
Avoid strong rent-control cities like Oakland, Berkeley, San Leandro, Concord, Fremont, Union City, Martinez, Antioch, and others.
I've always found that suburbs with great schools are the best locations for long-term appreciation. Cities like Pleasanton, Livermore, Dublin, San Ramon, Danville, Castro Valley are worth consideration.
Let me know if you have any additional questions about the East Bay.