AirBnB is probably going to be your best value for staying downtown and walking into class. Prices can be lowest starting at $30 per night.
Next, are Hotels near the San Jose airport which are few miles away from downtown with prices mid-range. You have to catch the light rail which is a 10min ride to downtown.
Depending on dates, prices can range from: $100-200
Hotels near downtown but more expensive.
Depending on dates, prices can range from: $150-300
Information regarding the Light Rail Public Transport - http://www.vta.org
Gish (Next to hotels near airport mentioned) > Civic Center > Japantown > St. James (Downtown San Jose)