Cheap Apartments For Rent In Southwest Houston Tx . The average home rent in this city is $3,455. On average, section 8 housing choice vouchers pay houston landlords $800 per month towards rent. 2447 Connors Path Court, Houston, TX 77073 3 Bedroom House for Rent for from www.zumper.com The average home rent in this city is $3,455. A rental apartment in this city will cost you from $350 to. The average voucher holder contributes $300 towards rent in houston.