I had a 1 bedroom apartment in Southwest side of Houston couple of years ago. Free electricity and water. Washer and dryer in the room. 24 hrs security at the gate. Pretty quiet, gated community in the middle of not that good neighborhood. I paid less than $800 only.
There are lots of cheap apartments, but lots of trouble too.
If you cook at home, food is cheap.
You might hate the traffic though! lol