have u tried looking into hostels??? they r usually between 25 and 50...and have reasonable service. You really don't need a car, cos u have the BART and buses....good luck!!!!!😀
I'll second the Carl Hotel recommendation. It is walking distance from the school and lies directly along the N-Judah Muni stop so you won't need to rent a car.
Any fan of Japanese culture can try Hotel Kabuki. It's right at the center of Japan town 👍, has a nice Sake bar 👍👍, and is very close to great JP restaurants. 👍👍👍 It's not cheap, though. (4 stars) 😉