Despite the fact that downtown Cleveland was rather quiet on weekends when I lived here briefly long ago, Public Square was always a focal point for large demonstrations and gatherings, and was also a busy spot in the warmer months for folks eating lunch outside or taking a break from work.
These days, it's been revamped to unify what was once four quadrants surrounded by traffic into two halves, one with a reflecting pool closer to Terminal Tower, and another with a large green space near the Key Bank building. It's a much more inviting space as a result and coincides with what's been a gradual enlivening of downtown. A much nicer space than before for folks to gather and rest.