Welcome! Here are some places where I’ve enjoyed (mostly cheese) pizzas or slices somewhat recently. I live in San Francisco and all of these are in the city:
Pizza Shop in the Mission - probably the closest to NYC style in the Mission these days since Arinell has shut down? Arinell still has a location in Berkeley if you are in Berkeley.
Angie’s, also in the Mission - I had a very good cheese pizza here. Thin crust and crisper than a Neapolitan.
Tony’s Pizza Napoletana in North Beach has a really good Neapolitan style Margherita.
Outta Sight Pizza in the Tenderloin - I had a good cheese slice here a few weeks ago. NY style.
For a Detroit style cheese slice, I like Square Pie Guys (multiple locations) and Cellarmaker House of Pizza in the Outer Mission.
Also check out the SFBA pizza thread: