Falls at Highpoint Apartments for rent in Dallas, TX on ForRent.com: (888) 213-4589 - Availability, pricing and special promotions subject to change daily. Welcome home to luxurious and comfortable living at he Falls at Highpoint, located one block south of the intersection of I-635 (LBJ Freeway) and Greenville Avenue in Dallas, Texas. The Falls at Highpoint gives you unparalleled and convenient access to all areas of the DallasFort Worth Metroplex.