@ cicoree: Congratulations on your husband's acceptance! The Bay Area is an incredible place to live... but also incredibly expensive. Unfortunately, one would have a very difficult time even renting a room within half an hour from Stanford for less than $1000/month; studios and 1 BR apartments would definitely be out of that price range.
If you haven't used PadMapper.com yet, I highly recommend it; it's a fantastic map-based aggregation of rental listings. If you're willing to live about a 30 minute drive away from Stanford in the even more suburban East Bay (ie: Hayward, Castro Valley), you can find a 1 BR for about $1000, though one should note that this is across the Dumbarton Bridge, with $5 toll (or if carpooling during peak hours, only $2.50). Closer to Stanford, as you toggle the 'rent range' up from $1000 to $1500 or $1600, you'll finally start to see 1 BRs appear in the vicinity of Palo Alto (namely in Redwood City and Mountain View). It looks like $2000 before you find your own 1 BR in Palo Alto proper.
With all of that said, Stanford obviously has many grad students, a large number of whom I imagine are surviving solely on their stipend; there must be some way to do it! Does his program offer on-campus below-market housing for grad students?