In California, cities are totally independent of school districts (except in that San Francisco is a combined county and city and its city counsil and mayor are also its county board of supervisors, and county boards and the state school board both supervise school districts).

School district funding in most districts is property taxes supplimented with state funds to a specific level per student. There are a small number of school districts that have property tax revenues above that, but most don't. IIRC, in the sf bay area, Santa Clara, one of the Palo Alto districts, and maybe one or two others are not getting state funds, but I think Cupertino is on the state funding schedule, and is well regarded.

Only the hardest hit counties like Fresno saw property tax decrease in the 2008 time frame. Although market values dropped, many properties were still below their capped assesment, and so their taxes would increase either by the yearly cap or because they were sold and triggered a fresh assessment. I don't know about other counties, but Santa Clara's assessor did assess down automatically; but the tax rolls still increased. So in that way, it's a lot more dependable than an income tax.