Apartments For Rent Near Houston Tx 77004 . Apartments in southwest houston $1,150. Check out 5,817 verified apartments for rent near the 77004 zip code, tx with rents starting as low as $650. Haven at Main Houston, TX apartments for rent from www.apartmentlist.com Right around the corner from the houston neighborhoods of rice university, the museum district and west university. Search by city, state, property name, neighborhood, or address. 2619 canfield st apt 3, houston, tx 77004.