Saint Peter's Square is dramatically beautiful. In the 17th century, Gian Lorenzo Bernini designed it to welcome people to receive the Pope’s blessing.
The most spectacular feature is the elliptical colonnade, which stretches out from the basilica’s facade. Two hundred eighty-four columns form the colonnade, creating an optical illusion. Look for the marble circle inlaid into the ground near the central obelisk to witness the illusion. Stand on it, and the columns appear in a single row, even though they are staggered and set 4 columns deep.
In the center of St. Peter’s Square is a 4,500-year-old red granite Egyptian obelisk. Nearby are twin fountains. Remarkably, they are almost identical, even though they were built 60 years apart.
My favourite time to visit the square is first thing in the morning when the golden light of the rising sun makes St. Peter's Basilica glow. It is also lovely (and almost empty) after dark when the basilica and its two fountains are lit up and beautiful against the night sky.
The square is free to visit and always open, although there may be some restrictions at night on how close you can get to the basilica.
You don't need a tour to visit, but if you want to learn more from an expert, suggest the linked tour, which is combined with a skip-the-line tour of the Vatican Museums (Note: this tour does not include St. Peter's Basilica).