Any affordable and safe neighborhoods (for single, renting) near 77007?

I’m a fresh graduate and I’m living around 30 min away at the moment (from this location). Work is too far away and my rent is too high (1200, mainly bc I moved from out of state and didn’t know anyone in the area). Also have some financial problems so I’m looking to save money by finding a month to month living situation somewhere in 77007 or close by.

Or at least a safe and affordable location. Budget up to 800/mo.

I also have a car do a place that wouldn’t have my car broken into would be ideal.

Ik this is a lot to ask for (within 800 bucks) but this wanted to shoot my chances anyway and see where it goes.