Regarding your questions:
"Buy or rent?"
This is your key question and it requires intimate knowledge of your financial capacity which no one knows but you. Hence, most of the answers you receive will be missing key variables.
"What does the yearly tax bill look like for a home priced around $290k in the Concord area?"
1.25% is a common "quesstimate"; however, your effective property tax bill actually consists of three separate levy categories: General Tax Levy, Voter Approved Indebtedness and Direct/Special Assessments. See: "Estimating Property Taxes in CA" http://tinyurl.com/bjjledz
for a thorough review.
"Please give details on fees, etc. Cali has..."
Details can only be provided based on the purchase scenario and what has been negotiated between Buyer/Seller. This said, in general, Buyer closing costs are 2%-4% of the purchase price. Lender points and origination fees can be a big factor in pushing total cost upwards. You can reference the calculator link below for reviewing closing cost scenarios:
"I might rent the house out here and rent in the Bay until I can afford a down payment for another home. Is that wise?"
1) Unless you are an avid saver with "extra cash", you will likely need the proceeds from a sale of your current home to buy in CA. Strategically; I believe it's best to have the cash immediately available if opportunity presents itself rather than the delay of placing your property on the market. Of course, this depends on your personal timing.
2) Conventional "landlord wisdom" is to own rentals within an hour's drive from your primary residence. A Property Manager can reduce risk, but it comes at a cost.