Well $1000.00 is plenty for an apartment. You can get atleast a 2 bedroom maybe even a 3rd. Below is a list of homes and studios for your budget. Eric gave you a good resource for apartments.
There are many apartment complexes that go for $850.00 for 2 bedrooms. Specifically I have a friend in a complex on the corner of Azavedo Drive and San Juan Avenue in Natomas. Decent area. I would say middle of the road.
Now for non-apartments. These are in nice areas.
These start at $750.00
http://www.sacrentals.com/goinside/whiskeyhill/Here is another rental for $750.00 In Land Park
http://www.sacrentals.com/goinside/1131-markham/$850.00 in Midtown
http://www.sacrentals.com/goinside/2430-q/studio/Here is one just a tad over $1k at $1079.00 This is right near Sacramento City College. Very nice area.
http://www.sacrentals.com/goinside/2102-11ave/