Groceteria.com

Randalls never really made it big until the early-mid 80's, and I personally never heard of them until that time. But I heard about a 1975 Randalls on I-45 somewhere which has since closed. Unfortunately the current tenant is unknown to me and was not in my source. Did Randalls from this period have any identifying features?

Not really. The logo was rather generic, and there's a video linked somewhere from one of these Texas archive sites of a 1970s era Randalls. It wasn't particularly special, ugly block-letter logo, brown brick building...Randalls was only established in the mid-1960s, which is much newer (comparatively) to its competition. Their later post-1980s stores were more distinct.

The I-45 one might have been the one moved to Kuykendahl and I-45 in 1997, which has also since closed. Sadly, only their post-1990 stores were especially distinctive (New Generation), and that distinction also went away under Safeway's ownership. Complicating this was their acquiring several AppleTree stores, which were all built under Safeway and were distinctive, though many of those have since closed.