That house gets a bit of a premium for the view of the bay. It is also close to the parks and the elementary school. Probably adds $3-400k to the price.
As for the hypothetical, I would take the bay area over Dayton, Ohio under any set of facts. The weather in the bay area is delightful. The weather in Dayton is dark, cold and dreary from about mid October to mid April. Then it is 90 deg and humid for about six weeks. I lived in Ohio for 11 years. There is nothing in Dayton. Nothing. A better hypothetical would be Cincinnati or Columbus. Dayton is just dreadful.