I was just in Rome last year. The only place I really ran into issues was outside the Coliseum. I just said “huh” and mumbled “I don’t know” to every question until they went away. “Where are you from?” “I don’t know.” I think they just thought I was an idiot, or had very limited English, which is fine by me.

I was told later by a guide that if you say “no, grazie” in a semi-convincing Italian, they’d assume you’re local and leave you alone.