Now I went and did it, bought an old DeSoto/Plymouth dealership!

Its a no brainer. Use it for classic car storage, but more than that, it could be a country club for car guys who need a place to hang out other than a golf course for a monthly membership fee. With a party room, local car clubs could use it for special events (hook up with a caterer and you could host other events).
Here's a place in Maryland that does the car storage. The most difficult part of this type of business will be insurance. Your coverage will need to change as the value of the vehicles being stored changes. You may think twice before allowing a $500k+ 1955 gullwing Mercedes or 1935 V16 Cadillac into the place. Also there will be steep liability insurance rates if you allow customers to work on their own cars there. But for the most part, people who pay for storage are not likely to want (or have time) to do more than changing their oil or rotating their tires.
Collector's Car Corral | Luxury & Classic Car Storage Facility | Collectors Car Corral
Here's a place in Florida that uses a personal car collection and garage for weddings and special events.
Horsepower Events

Of course you'll want to start locating replacement signs and fixtures to recreate the original look as well. Nice that there was a gas station there too as restored gas pumps will be a great addition as well. A local AACA club member inherited the building his grandfather had built for a Nash AMC dealer and he has recreated the original look inside and out.

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