There is not a state law against it unless there are deer in the area (see the exert from the  IDNR Digest below for more info). But there may be a city ordinance against feeding geese. You would need to call the mayor's office or city council to find out.  Geese are herbivores, so it is better for their health if people do not feed them.    
According to the Illinois Department of Natural Resources Digest:  It is unlawful to make available food, salt, mineral  blocks or other products for ingestion by  wild deer or other wildlife in areas where wild  deer are present.  Except:  -- elevated bird/squirrel feeders providing  seed, grain, fruit, worms, or suet for birds or  squirrels located within 100 feet of a  dwelling devoted to human occupancy.  incidental feeding of wildlife within active  livestock operations.  --feeding of wild animals, other than wild  deer, by hand as long as a reasonable attempt  is made to clean up unconsumed  food.  --feeders for wildlife other than deer so  long as deer are excluded from the feed  in and around the feeder by fencing or  other barriers.  --standing crops planted and left standing as  food plots for wildlife.  --grain or other feed scattered or distributed  solely as a result of normal agricultural,  gardening, or soil stabilization practices.  --standing, flooded, or manipulated natural  vegetation or food/seed deposited by natural  vegetation.  -- grain or other feed distributed or scattered  solely as the result of manipulation of an  agricultural crop or other feed on the land  where grown, for purposes of dove hunting.  --food material placed for capturing or killing  wildlife pursuant to 520 ILCS 5/2.37, 2.30,  and 1.3.  --scientific permits issued pursuant to 17 Ill.  Adm. Code 520 that allow food to attract  wildlife.  --any other permits issued by the Department  of Natural Resources that require the  attraction of wildlife for purposes of management,  research or control.