$150/night is about as cheap as you'll find in the Bay Area. It'll be too small for a family, probably in a shitty area. A few years ago you might've been able to swing that, but now? No.
Btw, I did manage to find a 180$ per night deal in the bay area at Hyatt house, complete with a kitchenette and utensils recently for a friend.
At that price point in the city you've got options with, e.g. Travelodge, and you can choose between being right next to the freeway or in the middle of the meth epidemic. For a single occupancy room $150 would potentially get you something comfortable, but for moving a family? Not so much.