You don't need to be religious to appreciate the calming atmosphere of Annunciation Greek Orthodox Cathedral. Check when the next service starts or when it's open for general viewing.
You'll be spoiled for sightseeing choice when in Downtown Chicago. Annunciation Greek Orthodox Cathedral is a good place to kick off here, but there are loads of other interesting places to consider. Wrigley Field, Millennium Park, and Willis Tower are near the principal church and will top off your day nicely.