I had seen this postcard before on several occasions, either online or in an antique shop. It's labeled "LAKE VIEW PARK BEACH, LORAIN, OHIO" and I had always thought that it depicted the pre-tornado Lakeview Park bathhouse.
However, the recent article in the Morning Journal about residents having to maintain Century Park on Lorain's east side (because the city wasn't) sent me looking for a vintage postcard of the park online. When this one came up, I disregarded it as being Lakeview Park – until I took a closer look and realized it was Century Park all the time.
Here's my shot from last night. (I couldn't duplicate the postcard view exactly because I was already at the far western end of the park.)
According to the above article, the beach house has been there since 1928.