I would hope you can visit San Fran, it's a cool city to walk around in and see. It might be the only time in your life you would be there.
I don't see why it wouldn't work if you can find a reasonably priced hotel and just leave your bike there and get around on foot etc. When I was there a long time ago, it made sense even back then to not take a chance with my bike, and it's obviously more relaxing not to worry about it being stolen.
You're from Manchester so you should have reasonable "big city" common sense real life instincts or street sense when walking around.