The Drury Inn Union Station is the closest to Union Station (apart from the Hyatt which is *in* Union Station). It is just to the side, across the street from the train shed.
Now another tactic for your stay might be to stay at the Westin by Busch Stadium or the Sheraton St. Louis City Center and then use the light-rail train ("MetroLink") to and from Union Station.
Many conventions include a pass good for the duration of the meetings.
http://www.metrostlouis.org/MetroLink/stationlist.asp