It looks like that will be tough. If you put your criteria into Realtor.com, you can get specific listings. You can use google street maps to "look around" the neighborhoods once you have an address you are interested in. There are only 3 3-bedroom, 2-bathroom properties for $1000/month:
242 Winding Trail Lane ($1000)
725 Central Ave Apt B4 ($850)
383 Springview Lane ($965)
The lack of pictures suggests they might not be in great condition. I don't know anything about those neighborhoods, though. Good luck! :-)