I have found some very nice affordable homes in Hockley around $800-$850 and they are newer homes. It's also close to the Premium Outlets which is in Cypress off of Hwy 290. Good luck with your search and if you need more info on finding the right home, you can call me at 281 973 7424 (RICH), http://www.brandnewhomesinhouston.com. Have a great day!
You're making a long move. I'm glad you chose Texas. A few towns that are within about 30 miles from Brenham, towards Houston are Chappell Hill, Hempstead, and Hockley. I've never been in that area during "rush hour," but I doubt there is much traffic. The closer you get to Houston on 290, the more traffic there will be. Chappell Hill is only about a 10 or 15 minute drive from Brenham. It's a beautiful area with lots of bluebonnets, the state flower of Texas, plus other wild flowers along the roadside during the spring. As far as safe areas, I would recommend calling the police department of the various towns. They can provide that information. Do you specifically want an apartment, or would you want to rent a house if possible?
You can contact me at firstname.lastname@example.org and I'll be glad to help you. Best wishes for a safe move.
Century 21 Paramount