Argonne National Laboratory can be reached either from O'Hare International Airport (30-40 min. to drive) or Midway Airport (20-30 min.).
Driving directions and other useful information can be found at the Argonne visitor information site. Public transportation is virtually absent and taxi costs about $60 (not recommended).
Usual ways to reach Argonne are either personal car or Limousine service (about $40, to Argonne only).

Before packing check the weather forecast in Argonne area:

Lemont Weather Forecast, IL (60439)