Okay, so three problems:
1. You will need a parking permit to park the street at all. (I don't know what those cost these days, but figure at least $50/month for that. Maybe more.)
2. Finding parking anywhere in that part of SF is a total hassle. So you will need to alot time and you will probably have to park some blocks from your apartment--which is good for staying fit on those steep Nob Hill hills.
3. Cars sitting around in that part of SF will be broken into eventually. So empty everything you don't want stolen from your car and give them fewer things to rob. (Pull out radio is a good idea.) And be prepared to change a window once or twice a year.
4. (I lied, there are four problems.) Street cleaning once a week means if you don't want a bunch of tickets you will need to move every week to an non-street cleaning zone.
My suggestion: either nix the car (good for the environment) or find it a proper home in a garage either in your building, in SF (expensive) or maybe in a garage in the East Bay.
Okay, have fun in Nob Hill--that part of SF is a blast! Even though on practical terms it can be an expensive pain the neck.