Be honest: are there apartments with a max rent of $1,000 in non-sketchy neighborhoods?

I'm moving out of my current place in April 2025, but I want to get a jump on finding possible apartments. It's a house that I share w/ two other people, rent comes out to around $1,000 including utilities, trash, pest control, etc.

I don't make a ton of money- I've calculated that my take-home after taxes and benefits each month is about $2,600. My worry is if I get a less-expensive apartment closer to downtown, where I work, that I'll be in a sketchy neighborhood. I'm eying a place on east riverside, but I've heard bad things about the area.

I only ever lived on-campus when I was at UT, so I didn't get a good feel for where the better areas to live are.