JEFFERSON HEIGHTS APARTMENT HOMES IN HOUSTON, TEXAS brand new apartment homes in Houston, Jefferson Heights is where downtown edge meets heights style. We have modern Apartment Homes for the Urban Explorer. Where downtown edge meets Heights style sits Jefferson Heights - modern apartments for the urban explorer. Surrounded by century old homes, active urban parks and thriving nightlife, Jefferson Heights caters to hip professionals immersed in the timeless trend culture of the Heights neighborhood. Jefferson Heights is a blend of lifestyle and personality as unique as Houston itself.