$150/night is about as cheap as you'll find in the Bay Area. It'll be too small for a family, probably in a shitty area. A few years ago you might've been able to swing that, but now? No.
When you are moving, you don't have to stay bang in the center of bay area. You can stay in Dublin or Morgan Hill while you look for a year long lease in the bay. Also, I moved 10 years ago. 20K to move is an absurd number that the poster pulled out of his ass, along with "living in dozens of states".
Btw, I did manage to find a 180$ per night deal in the bay area at Hyatt house, complete with a kitchenette and utensils recently for a friend.
You could stay in Fresno too, but the point is staying in a hotel in the Bay Area is expensive. A decade ago things were significantly less expensive out here.
Sure you can find hotel rooms for $150/night, but for moving a family? As I said they're going to be too small or in too rough of a neighborhood. For instance the Extended Stay in San Rafael starts around $120/night after all the taxes and fees. It's also downwind of a sewage treatment plant, right next to 580, and in a fairly industrial area.
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.
