As above fly between places but rent car to explore in Mass and California. Credit card airmiles, Amex is very good for BA but you need to decide which airline you’ll use.
Cape Cod is lovely, good for family. Explore a little the towns on the inner and outer coast plus you must see the dunes and take a whale watching trip from Provincetown (is season dependent). If you have time explore a bit, Newport, inland to Vermont possibly. Boston is a cool city, acquarium is great.
Chicago is fun city, enough to amuse you there without needing to venture too far. Lovely weather in the summer, absolutely arctic in the winter.
St Louis I don’t know but a fun contrast to other cities I imagine.
California is the huge variable, north or south you don’t say. I’d say spend the most time there and explore by car. LA, San Fran (and the home of mtb), wine lands, Yoesemiti ? People would easily spend 2 weeks touring just a part of California.