The central part of Rome has an ancient layout, which is literally studded with piazzas. And many of these city squares have fountains, large and small, unknown and famous.
Another part of the scene are the cafes, which are packed on any Saturday or Sunday afternoon. The deal is to find your favorite place, nab a good table (in front, of course), order food and drink, and just relax and take it all in. Time slows, stress disappears, and life is good. I suspect that each person has their own criteria for what makes the piazza “the best”, but for me it must have a fountain.
Fountains in the piazza go back to the Roman Empire. Water was not only essential, but was an integral part of life. Aqueducts were built to bring it to Rome, and your position on the economic and social ladder determined how it was used. Wealthy Romans had heated baths and garden fountains, but the majority of people were happy to visit their local fountain for fresh water.
Fountains in Rome today are much less serious. Now they are high art, a tourist attraction, a place for your dog to get a drink, or a destination to relax and enjoy life. Mostly, they are fun.