The Heights Apartments for rent in Omaha, NE on ForRent.com: (877) 295-2487 - Availability, pricing and special promotions subject to change daily. The Heights Apartments featuring one, two and three bedroom floor plans in Southwest Omaha with a convenient West Dodge Street location. Amenities include bay windows, eat-in fully equipped kitchens, garages, 24 hour fitness center with sauna, sparkling swimming pool, billiards room and playground.br br br Don't leave your cats behind they are welcome too! Some units boast separate formal dining rooms, fireplaces and washerdryer hook-ups. The Heights is in a convenient location just off of 120th and Dodge Streets, with easy access to I-680, and the area's finest shopping, dining, and entertainment. Our friendly office and 24-hour maintenance staff are always here to serve you.