Kinda depends on your priorities. leoduncan posted the most economical, but I recommend you get yourself to Navy Pier and take the water taxi (or whatever they call it) from there to the museum campus. Some goofy stuff at Navy Pier- especially if you have kids along- and a great view of the city from the boat.

This link #mce_temp_url# shows options from Great Lakes to the city. Train takes you to Ogilvie Center. If you're up for a hike, head east from there, up Michigan Avenue and east again to Navy Pier and water taxi #mce_temp_url# as mentioned above. A shorter hike to Union Station and you could water taxi to Navy Pier.