I agree with the other reviewer that $150 is a pretty low budget for a bike. But if you only have $150, a cheap bike is still better than no bike. Since you are riding mostly roads, it should hold up for a while. Just don't expect it to hold on mountain bike trails.
Either go to a department store or search for used bikes (craigslist has a lot). I doubt bike shops carry bikes that cheap. I would use craigslist because you will get a better bike for the money. When choosing a bike, do not even consider full suspension, which lowers the quality of the bike. Front suspension is very common now, but if you can find a fully rigid bike it would be nice since suspension is only needed on dirt trails, not roads in SF. A rigid bike with no suspension would have better parts than a bike with suspension. Also, bikes this cheap usually come with suspension that does not work very well. I'm not sure if you can get an old road bike (I assume that's what you mean by racing bike) for the price, but it would be nice. Otherwise, try to get a hybrid. If you can't find a hybrid either, then get a mountain bike. Make sure the bike has gears, unless you want to climb the steep hills in SF singlespeed. Most importantly, test ride the bike before you buy it so that you are sure nothing is broken and that it is working correctly.
Good luck