Sterling Lindner Davis Department Store

Sterling Lindner-Davis Christmas tree, 1936
Located on grand Euclid Avenue at East 13th Street, this department store was a conglomerate of three other stores (hence the mouthful of a moniker) and as you can see, they always had a very large Christmas tree. Sterling Lindner Davis began the tradition of putting a stupidly enormous Christmas tree inside their atrium, starting in 1927. Legend has it the tree grew a foot while inside the store.

From a 1952 postcard:

A live, 50 ft. tree, festooned with 60 lbs. of 'icicles', 1000 yds. of tinsel, 1500 ornaments, and illuminated by 6 banks of 750 candle-watt spotlights. It requires 650 man-power hours to trim by swinging stages suspended from the skylight.

Their "Santaland" included a device where you could insert a coin and receive a gift that came down a slide, a train, and an enchanted forest display.

Update September 2023:  The former Sterling-Lindner Building is now home to the City Club of Cleveland.

Sources:
Cleveland Christmas Memories (about.com)
Encyclopedia of Cleveland History
Cleveland Memory Project
POSTCARDY: the postcard explorer