Chicago.
Yes, Southwest has flights every hour that go to Chicago from St. Louis. If you book it early enough, you can get a round trip for less than $200. They also offer deals on hotels and car rentals if you book through them.
Milwaukee is about 85 miles farther away then Chicago.
St Louis
NO
Illinois River
297 miles.
American and Southwest, to name two.
It is approximately 517 miles from ElDorado, Arkansas to St. Louis, MO and then another 298 miles approximately from St. Louis, MO to Chicago, IL. See related links for more details.
Checkout http://www.apartmentlinks.com/MO-St-Louis/apartments.html to find some good collection of St Louis
no. There is no direct train to St Louis from Indianapolis. however, you can take a train to Bloomington IN, or Chicago IN, and then to St Louis. at least that iw what I'm told
Heavens no. Chicago is about 350 miles away.