If doing all transit (for future reference), buy a $2.25 transit card at the Midway station, take Orange Line to State/Lake, go down the stairs and take a #29 bus northbound on State towards Navy Pier. Disembark on Illinois St. at McClurg Court (before going under Lake Shore Drive), walk three blocks north and one block east. Or, if you're easily disoriented, you could go to the Navy Pier bus terminal -- can see the W LS just north and west from there, and take the sidewalk/bike path over. (That walk's about an extra block.)
If taking a cab, any of the Orange Line's Loop stops should be fine -- I'd get out at Clark/Lake, really. It's further from the W LS but has elevators.