Our family of four is planning a three-four week holiday in June 2018 with art and culture, food and architecture with emphasis on Frank Lloyd Wright. Either northern Italy, Slovenia & Croatia, or east coast US. E. Liu, Dulwich Hill NSW
These are two really great destinations, either of which would satisfy your criteria.
Price wise there's not going to be a huge difference.
Your European itinerary gives you more breadth and variety, combining culture with some sensational alpine regions as well as coast, and a deeper historical dimension.
There's the beaches of the Dalmatian coast in that equation and the possibility of walking in the Dolomites which might appeal.
On the other hand, New York City, New England and the museums and cultural institutions of Washington DC add up to a power play that you'd all find stimulating and enjoyable.
If Wright's work is a major fascination, apart from New York's Guggenheim you'd have to include Chicago in your itinerary.
My own interests would tilt me in favour of Europe, but if the rest of the family voted for east coast USA I'd be happily swayed.