5737 N. KENMORE APARTMENTS IN HISTORIC EDGEWATER. Located just steps from Thorndale Beach and minutes from Lake Shore Drive, 5737 N. Kenmore Apartments is truly one of the most desirable and affordable apartments one can find in Chicago.This 7-story brick elevator building features 74 units comprised of affordable studio and one-bedroom apartments. All units include electric and heat. The building also offers a bike room, on-site laundry and a furnished lobby. Edgewater is a quiet, long historied neighborhood located on the north side of Chicago. Located literally steps from Thorndale Beach, you can relax at the end of the day with your feet in the sand or go for a run along the lake. Whatever you choose, this is a neighborhood you can truly call home. 5737 N. Kenmore stands as a beacon of classic, vintage Chicago architecture. This elevator building has been beautifully maintained and constantly updated. An on-site building engineer ensures that building maintenance continues to run smoothly.