As an example, individual room rentals near Stanford University can be found for $750-$900/month on the Stanford off-campus housing page. Meanwhile studios / single bedroom apartments generally are in excess of $1,300+ a month.
$800 a month is very tight. I've seen homeowners rent out a bedroom to a student but that is about the only way I've seen to get the rent that low.
Occasionally the parents of students have bought condominiums for their children to use while attending college. They rent out the extra rooms to other students keeping the cash flow down. With interest rates low, it can be a good choice but you don't want to be in a position to be forced to sell the condominium immediately when your student graduates.
Real estate sales statistics for Santa Clara and other cities can be reached from:
The average price for a Santa Clara condominium is about $500k.
Top 2 agent nationwide at Keller Williams Realty
Over 30 years experience
Over 1,000 homes sold in Santa Clara and San Mateo Counties
Sadly, I think that $800 is going to be tough for a studio here in the areas where you've specified. A room within a home shared with other renters is more likely at that fee, but a studio is going to start at $1000 per month or more. Keep in mind that, with so little rental housing available right now, rents are escalating almost as quickly as home's prices.
So check on Craigslist, or better yet, have your son check with the local college community housing boards and groups to find suitable housing. Remember, NEVER rent from an agent or owner who is NOT local. Never rent from people who claim to be out of town or out of the country and who want outrageously low rents for the home, and never rent from someone who can't show you a home unless you send him/her money first.
Be careful and be safe when searching for homes.