Website Cinema Treasures, a website devoted to all things US theater, has the story:
http://cinematreasures.org/theaters/31544
“The Suburban Open Air Theatre opened on October 6, 1950, featuring the musical comedy “Three Little Words” with Fred Astaire, Vera Ellen & Red Skelton. It was operated by Blake Lancaster and in 1955 it was owned and operated by David R. Brown and Exhibitors Services Company from Jacksonville, FL. Its parking ramp could hold 490 cars. It was expanded to hold 600 car in 1955. On October 3, 1955, David R. Brown died and the drive-in theatre remained open. The Suburban Open Air Theatre was closed on December 8, 1956.
It reopened as the Suburban Drive-In in May 1960. I believe it was bought by Super 50 Theatre Corp. (Iselin Theatres from Albany, NY). They were listed as owners in 1956. Iselin Theatres also owned and operated the Trail Drive-In at that time. In early-1967, General Cinemas Corporation was the operator of both the Suburban Drive-In and the Trail Drive-In. The Super 50 Theatre Corp. (Iselin Theatres) closed the Suburban Drive-In in November 1969 and the property was sold to Casto Development from North Miami. The former Suburban Drive-In is now a Best Buy and Lowes Home Improvement store.”

I know this area where 41 turns back south towards Sarasota. I believe there was a strip shopping center in between the drive-in and what is there now. I just can’t remember what was in it.

If you remember, please leave comments below.

(This is part of the Swampy’s Florida Floridana collection.)