Super H mart, possibly out of your range, has a LARGE drive through (some parking spaces covered too) and a food court, or a covered walkway (how far can she walk?) around the corner to Arirang Korean BBQ. If you want company, I might join you for the BBQ.
--Any strip mall with a LARGE supermarket may have a covered area for loading groceries, and a covered walkway to restaurants.
Mariano's at Golf and Waukegan has an awning extending out over the driveway and a food bar/area. Light rain and no wind only.
Joong Boo Market at Central and Milwaukee had signs for an underground garage (which I have not been in) and cafe restaurants on the 2nd floor (elevator was not yet working when I went, just after they opened), so research required.
The Glen in glenview has a parking garage from which you can at least get to the movie theater, and through it to ben and jerry's but I don't know about the adjacent restaurants (some may have a back entrance to the garage), so more research required...ans you could go to a movie too.
--Any shopping mall may with a garage may have covered access to restaurants.
--Let your mouse do your walking. Just scroll around in google maps, then if something looks promising (restaurant sounds good and parking looks promising) switch to satellite view and see if the pavement goes under, or at least right up to, an overhang. Double check by going to street view.
--Carey aka underdog