I have a single unit in San Jose. Up until July, 2017, this was not locally taxed. However, I received a notice that San Jose implemented a tax on all rental units, even for landlords that had 2 or fewer units in the city. It is just under $200/year. Just an FYI if you haven't gotten a notice.
Thanks @Jennifer L. , I just recieved this notice from City of Riverside as well after a recent 4 unit purchase. Definitely didnt see that coming