I think - but not 100% sure - that there used to be such an opportunity in or near Borghese Park but has long been gone. Someone asking about this quite a long time ago, turned up nothing either.

I too have never seen one over Rome - I somehow doubt it does exist in the city or too nearby.

Yes, a couple of years ago there was indeed a balloon in the Villa Borghese park and you could go up in it. But you didn't get far up as it was well ancored to the ground! So no actual "ride" took place - you just got a view from a higher point... I too confirm, never seen a hot air balloon in the sky of Rome, except on 1 occasion (in more than 10 years of living here) but no idea what that was about. I immagine it may had to do with some form of PR or maybe for a film?

I would be very surprised to see a hot air balloon ride over any large city. Doe anyone know of any in other large cities?

Balloons often don't land where they're supposed to. When I lived in Princeton, NJ, there were frequent hot air balloon rides over the open country, but one of them once landed partially on a neighbor's balcony, with the basket dangling above the ground. The local fire company had to intervene, and fortunately no one was hurt. But immagine something like that happening over the Corso Vittorio Emanuele II.