Paul - here's my list of suggestions:
Sears Tower / Hancock - like other comments I prefer the Signature Room for lunch and great views
Millenium Park / Cloud Gate - [y]
Lincoln Park and the zoo is a great place, the zoo is small, lovely building and a really cool big cat house
Alongside Lincoln Park is RJ Grunts - home of chocolate cheese (oh and good burgers, no reservations, queuing around the block on busy days
Pizza - Chicago has great pizza restaurants, my current fave is Pizza Due (again no reservations and heaving), the original Gino's East is more touristy but has fascinating walls
If time allows the Frank Lloyd Wright houses in Oak Park and the tour you can do of them and his home is great - if not then the river architectural cruise is fantastic and shorter (but if it's cold may not run due to frozen waterways!)
Michigan Avenue shopping, totally - Water Tower Place, Shops on North Michigan, the North Bridge malls could each keep you busy - and RL is very nice to stop for lunch (and watch the ladies wot lunch)
The Art Institute is stuffed full of treasures, it's also bigger than it looks!
Restaurants - a visit to Chicago may not be complete without a steak! There are a number around Ontario / Dearborn including the home town Ruth's Chris, Smith & Wollensky and the Chicago Chop House (my fave) - just beware portion control! Tru is more upscale but very highly rated and good!
Oh Wrigly Field - yes!
There's a plane at JFK, to fly you back from far away
all those dark and frantic transatlantic miles