Might check the past City Directory, a publication that has cross references by names, addresses and phone numbers.
Might check with business licenses office, they may have records by address.
Check the Assessors office for business personal property records.
Look in the property records for filed notices of lease agreements.
I'd probably just ask neighboring property owners who they remember being in there.
Old timers usually know who use to be there. I can recall most businesses along the main drags of town back to the 60s, but not the malls, they change too fast to keep up with, some are gone before you notice them. :)
Look at the review sites such as yelp or google. Sort it by oldest comments. The reviews are an important metric when analyzing a tenant. Some older comments will mention I remember when this place to be an xyz joint etc.