Whether your island needs a building permit is something we check with the city for each job, not something I'll guess at. The city's Engineering Division does issue a separate encroachment permit for any work in the public right-of-way, like a curb cut or a driveway change. When a job needs a permit, we pull it and line up the inspections.
When the city does review a project, a complete site plan shows public easements, how far existing patios and retaining walls sit from the property lines, and the size, location and setbacks of the new work. So I measure where the island will sit against the lot lines early. The State Fire Marshal has also mapped fire hazard zones in Antioch, and it's worth knowing early whether your lot falls in one.
Most islands we see here go off the back of the house, on a patio or right beside one, often with a path back to the kitchen door. We're based in Antioch and do the same work in the cities around it, from Concord and Walnut Creek out to Brentwood and Rio Vista. Not sure we cover your address? Call and ask.