In the beginning, back in June of 2013, Toby Shine, 71, was thinking he needed a little space, sort of a man cave where he could gather with some friends and talk about the glory days, and cars. Lots and lots of cars. Like a couple million dollars worth of classic beauties.

Shine’s collecting journey started at age 16 with the purchase of a 1947 Dodge business coupe. Shine and his wife, Sylvia, operate Okoboji...