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.

https://www.airbnb.com/s/San-Jose--CA--United-States

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

http://www.vagabondinn.com/vagabond-inn-san-jose 

https://www.wyndhamhotels.com/wyndham-garden/san-jose-california/wyndham_garden_san_jose_airport/overview

https://www.ihg.com/holidayinn/hotels/us/en/san-jose/sjccc/hoteldetail

Hotels near downtown but more expensive.

Depending on dates, prices can range from: $150-300

https://www.destinationhotels.com/hotel-de-anza

https://sanjose.place.hyatt.com/en/hotel/home.html

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)

http://www.vta.org/routes/rt901

http://www.vta.org/routes/rt902

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