you are NOT going to find anything that meets your basic requirements.
rents in that area in decent neighborhoods run $2000/mo and up, unless you get lucky.
here's a link to Craigslist, south bay area, to get some ideas http://sfbay.craigslist.org/sby/apa/
I would have to say the best areas near Santa Clara are Milpitas, Los Altos, Saratoga and Los Gatos.
you should find a rental agent/reactor as soon as possible, unless you find something on Craigslist.
if you don't mind a little bit more thanXXXXX I would strongly suggest Morgan Hill. you could get a nice 2 br /gar and pool apartment for under $1500 6 years ago (when I left).
let me know if that helps.