The park closing time currently varies depending on the season and daylight hours. It is 5 PM in winter and up to 8 PM in summer. You can check it (and get a good trail map) at co.sanmateo.ca.us
It opens always at 8 am. If you need an earlier ascent you can use the Old Ranch Road Trail (and avoid the parking fee) which will give you a 2 mile one way all trail approach.
San Bruno Mtn is not San Mateo County's high point, but it IS the most prominent peak in the county. It is ranked #53 of the 58 counties in prominence, as listed at Peakbagger on its california county prominence peak list