I would do New York as everyone should visit once, then tag on short flight to Miami Beach afterwards for some sun/pool time...
I love California and have tagged it o.to the end of long US trips but I think it stands alone as a destination...avoid LA and go to Orange County, especially Laguna Beach. Absolutely stunning, great food and art scene and wow see how the other half live.
Unfortunately I wouldn't return to Portland Oregon or Seattle, the homeless camps there were so sad to see and I'll be honest a bit scary. A lot of mental illness on the streets. Also the weather in the Pacific North West can be a little gloomy.
Loved New Orleans and would return, not sure it's great for kids though. It's boozy and foodie and cultural, but I imagine kids would be bored.
Boston definitely felt the most chilled and was less of a culture shock and I would love to visit New England.
Based on your requirements and that it is a first trip, I would do New York and Miami Beach personally but Miami Beach isn't the safest and is not to everyone's taste so its hard to say. Maybe a New England road trip would be a bit more family friendly to be honest.
Vegas is good fun but 0 culture. Still could be a great holiday. But nightlife obviously does play a big part.
Can you tell i am passionate about this subject :-)