Can you get a closer view?

Looks a lot like Magnolia grandiflora to me.

Me too, Magnolia cone, with little red seed when mature. This followed the early magnificent white flowers.

The tree looks like a Magnolia, but the fruit says otherwise. I'm sorry the photo isn't focused on the large fruit. They are glossy green, like a large Bell Pepper, about 5 or 6 inch long. You can see many in the photo. I clue: An Italian worker at the hotel kept pointing to the glass ash tray on my table when I pointed to the tree. She was talking about the tree. I have no idea what she was saying.

It is indeed a magnolia. Botanically, you are looking at strobili, a kind of inedible fruit.

No doubt about it, Magnolia grandiflora with seed cones. Later these turn pink, the individual compartments (carpels) split open and orange seeds hang out on white threads.

I'll bet that the glass ashtray was a model of a magnolia blossom....maybe?