The switch from small talk to "lets spend the next two hours together" is a bit hasty. As always, Italy looks beautiful (even in black & white). I couldn't imagine anybody wanting a "friend" who knocks down everything as Joan's Maria. Kinda too much like a tourist publicity at times, the titles of the cities not helping.
SPOILER AHEAD: I don't know of they couldn't have stayed together, but I sure didn't like her stating the reasons at the airport gate. The name does hint it's not going to last.
PS (non-spoiler) On the plane to New York he asks the man next to her if they could switch seats and he declines. How about she exchanging seats with the woman next to him?