The weather between the months of November and March are absolutely lovely in Kuwait and allow for one to go on long walks. These are some routes I have taken and the sites along them:

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)

1. Maqsab Gate
2. Jahra Gate
3. Shamiya Gate
4. Shaab Gate
5. Sharq Gate

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