This car was owned by Carl Fisher, one of the founders of the Speedway, and apparently raced just like this with no body.
They also had several race cars that were made in IN as well as some generally historic Indy Cars.
The yellow one is the Mormon Wasp, the winner of the first 500 and also features the first rear view mirror which was integral to the victory.
That's the Borg Warner (Indy500) trophy along with the Penske Yellow Submarine. The blue car behind the trophy is Mark Donahue's Penske car.
They even had a little simulator there with the basic Thrustmaster Ferrari wheel. It wasn't on though.
Sadly, I wasn't able to take a lap but at least I got a pic of the Subaru with with the track (short chute into turn 2) behind it.