We also just returned from a July 4 week there. Didn't know about the boycott, sorry to hear that. Let's see...
There's a wonderful, huge supermarket a couple blocks behind the Hyatt, forgot the name, but the concierge will know - maybe that was Marianos. We rented the refrig too.
Used public transit from Midway and to O'Hare at 2.25, both were an easy walk.
If you sign up for Hyatt Gold, they'll give you free in-room internet (they did us, anyway).
Really inexpensive restaurant we liked, was recommended by a bus driver:
Ronny's Steakhouse, right at Clark/Lake subway entrance (how you get to O'Hare)
Moderately-priced restaurants we liked:
Purple Pig on Michigan Ave
Grand Lux Cafe on Mich Ave - where they'll bake your dessert fresh, if you order when you order the main meal.
Restaurant inside hotel was ok, as was an Indian restaurant 1 level down.
Tried to find free museums, but turns out that most are only free for IL residents. In any case, Art Institute was wonderful.
Hancock Tower - rather than paying, we went up to restaurants for free and looked out all the windows, then left because there weren't any window-front tables avail.
We sprung for Cirque Shanghai show on the Navy Pier and enjoyed it - buy the least expensive seats, you can probably move into the pricier ones because many were vacant, and the later in the evening the better.
Shedd Aquarium - pretty good but overpriced, and way too many crying/screaming babies in every area.
Did the boat architectural tour + July 4 fireworks - next time I'd just do the archy tour and go watch fireworks on my own. We didn't do a longer Frank Lloyd Wright walking tour in Oak Park, it was so blasted hot that week - in the hundreds - but it's supposedly really good.
Unfortunately the city moved Taste of Chicago foodie event from July 4 week to the following week, after I'd reserved this - too bad!! Rene, are you there now? If so I hope you're getting to enjoy that!