Mubarakiya: the historic market, here are just some of the sites
Kuwait City Souqs: often labeled as “brutalist,” you can walk between and visit them
Old Gates: I haven’t walked between the five historic gates from old city wall in a single go, but you conceivably could (although the route will be tricky at times)
Salmiya: outside of the old walled center of Kuwait, there are fewer historic sites but still plenty to see
Hawally: the part of Kuwait I live in, and so my favorite to explore, I’ve posted walking routes here & here
Ms. Moore Travels 