Besides the shortness of the flight due to supersonic speeds, it left quite early in the morning (around 7 am or so) which meant that it you were connecting in from somewhere else you needed to come in the night before – so only really convenient for those living or working in NYC.
Concorde at the gate.
I recall that the food and service were excellent (lobster omelettes with champagne, and attentive if very formal flight attendants). The seats were equivalent to domestic first class, seat pitch was around 38′’. Not much inside storage though, I remember the flight attendant had to take my backpack and store it somewhere so I did not have access during the flight. The ceiling is quite low, even in the middle of the aisle, so very tall passengers would have to stoop.
Looking across the aisle mid-flight.
But the view! Hard to describe but flying that high (around 56,000 feet) is noticeably different than flying a conventional passenger jet. Looking upwards the sky is a much deeper blue and if you looked closely you could see the curvature of the earth.