My thought is that you must find in advance an agreement on what you mean with the words "eating well".
-Do you eat well in a place where the widest range of different culinary experiences can be made?
-Or in a place where there is the highest number of top restaurants?
-Or in a place where the average quality of meals is good and you're sure to eat well at any price?
The answer depends on your personal choice about this point.
I mean that great, rich, multicultural cities like NYC or SF or London could be considered the best if your answer is 1 or 2...but if your budget is low and you can afford only economic meals probably you'll not eat that well as the local culinary culture leaves a bit to be desired

On the other side, in Italy you have a lot of top restaurants and can also get almost everywhere a good meal for $ 20...but only if you're looking for Italian food as ethnic restaurants are lacking (immigration here is mostly illegal, only few foreigners are integrated and we cannot be defined a multicultural society yet). In example, Genoa (which has 800.000 inhabitants) has about 20 Chinese restaurants, 2-3 Arab restaurants, only 1 Indian restaurant

and no Greek restaurants
So, no Italian city can be defined "the best place for eating" according to point 1...
In any case, if I should anyway give an answer, for the above mentioned reasons I would say Paris!
Pongi