I am looking for somewhere in either the Chicago area or the
Indianapolis area that sells Toohey's New, an Australian beer. I would
like to purchase a six-pack, so I am looking for a liquor store, not a
bar that has some on tap.

You might ask these people in Chicago:
http://www.chibeer.org/

Sam's Wine & Spirits does not have Toohey's, new or old, which is a
bad sign, considering all the different beers sold there.

What about asking the Chicago Aussie Rules Football crowd?
http://www.chicagofooty.com/main.html

"Feel like a Tooheys,
Feel like a Tooheys,
Feel like a Tooheys or Two!"

So now there is Tooheys New, is there a Tooheys Used?

In my barmaiding days someone rang up and asked if the bottleshop sold
Carlton Cold, before transferring the call I commented that all the
beer would be cold.