Rome is amazing, so straight off the bat that piece of advice will not work for everyone.
And I have more examples: Cinqueterre is out of this world. In same cases it's true though: Florence left me unimpressed, but I think it was the fault of the huge influx of tourists and peddlers that ruined everything.
“Probably” does a lot of heavy lifting in my aforementioned rule of thumb. There are some major cities that are worth visiting despite the tourists.
In some cities, like London, the rule applies fractally. Avoid anywhere listed in tourist guides and there are lots of great suburbs to explore.
Whereas a city like Paris, great as it is to lay eyes on the Eiffel Tower and the Arch de Triumph, the city is ultimately a dilution of its former self. These days most major cities are very same-same.
IMHO if you want to visit Paris the city (vs. Paris the symbol), you can ignore the Eiffel Tower and the Arch de Triumph, which are monuments that have not much to do with the history of the city itself, and instead wander around in Montmartre / Saint-Germain / le Marais / islands de la Cité and Saint-Louis / along the Seine and the canal Saint-Martin.
And I have more examples: Cinqueterre is out of this world. In same cases it's true though: Florence left me unimpressed, but I think it was the fault of the huge influx of tourists and peddlers that ruined everything.