which airport- in western europe - would be the cheapest to fly into from Chicargo ?
Impossible to answer. No airport is necessarily cheaper. It depends on the airline, competition, and promotions. Check them all frequently to find the best deal.
Look into Frankfurt, Zurich or Geneva. if an airline is starting a new route as United did for Geneva from my airport the deals where alot lower.
Seasonal charters or service can also be the cheapest.
For example, Iceland air (through Reykjavik) is currently the cheapest from Winnipeg. It's an odd routing, but clearly the cheapest.
So from Chicago, it would be worthwhile to a dig a bit and look beyond the big American airlines and check to see if any European airlines are flying in because of their own domestic demand for flights to the US.
A year and a half ago I got a $500 RT ticket (total price including taxes) to Munich on Lufthansa, booked it on their website. But as said above, it just depends.
I don't see the point of seeking the cheapest airport to fly into. Won't you then have to pay for transportation to whatever your actual destination is? Or do you fly into the cheapest airport and then just wander?
It depends on WHEN. Until end of October Air India operate ORD to FRA at really low prices. They're a Star Alliance member and an OK to fly with airline. Other than that try Frankfurt on Kayak or so, also search for Iceland Air and Iceland Express connections to FRA or Brussels (their Frankfurt is Hahn and is right be the Mosel river)...