Choose from 0 available Assonet, MA townhomes for rent to find a floor plan that fits your lifestyle. Most townhomes are multi-level, with bedrooms located on the top floor. Some townhouses have basements for additional space, and some offer features like paid utilities. Be sure to view photos or take an online tour to find a rental that works for you! Some terriffic Assonet neighborhoods with townhomes for rent include East Side, Downcity and Western Fall River. If price is a factor, consider looking in nearby cities like Somerset, Fall River and Taunton.