Start with the lake
Head east for the lakefront, then decide how ambitious you feel. A long walk, a short walk, sitting and looking at the water: all legitimate uses of the place. The skyline does a great deal of the work. On windy days, the lake will remind you that this is not a decorative pond.
The zoo and the green bits
Lincoln Park Zoo is free to enter, with no ordinary admission reservation, which remains a rather lovely thing in a city where almost everything else has discovered a service charge. South of the zoo, the Nature Boardwalk gives you a quieter loop around the pond, with city views and room to slow down.
The nearby Lincoln Park Conservatory is the indoor, leafy option. Admission is free, but timed reservations are required, so book before setting off. The Alfred Caldwell Lily Pool is another lovely, quieter stop when open for the season. Check current access rather than expecting every green corner to operate on the same schedule.
Shopping, with occasional fresh air
Armitage and Halsted are good streets for a proper browse: little shops, clothes, things for the home, and the steady possibility of finding something you suddenly feel has been missing from your life. Clark offers another long run of neighborhood shops and places to stop. You are allowed to look without acquiring anything. In theory.
A small aside from David
One of my favorite local activities is watching Lincoln Park mothers pilot $1,200 strollers toward a pastry. These are not conveyances. They are small European vehicles with better suspension than my first car. The women operating them have somehow been to Pilates, answered several consequential emails, and dressed a person who cannot yet hold a spoon, all before I have located my glasses. I admire the competence. I am also a little afraid of it. There is a particular confidence involved in approaching a crowded café with twins, a golden retriever, and the firm expectation that this will all work out. Usually it does. I can barely get myself through a revolving door without a strategy meeting.