Design Travel Advice: Chicago & New Orleans

I’m about to embark on a trip to the US to visit some relatives - I hail from there originally but have grown up in Australia I haven’t seen to much of the states, so plan to use the trip to acquaint myself with some sights and culture. Currently the plan is to hit NYC, Chicago, and New Orleans, + relatives in Virginia (near Richmond).

What I’m looking for: Are any must see “design destinations” in those areas? I’ve already flagged Millennium Park in Chicago + MOMA in New York, but other than that I really have no idea what to look for? I know there are a lot of great consultancies but would one visit these places? It’d be good to do something other than just the standard museums and architectural sites…

Any tips would be much appreciated!