Apartments For Rent In Houston Southwest . Apartment rent in south houston has increased by 4.2% in the past year. The average home rent in southwest houston is $2,387. Decorating Your ApartmentApartments For Rent in Westpark SW Houston from apartmentswestchasetx.com Explore neighborhoods in central southwest, houston, tx. 4 beds 1,833 sq ft $1,512 / mo. Explore neighborhoods in greater fondren southwest, houston, tx.