Walk around The Vista. A classier version of 5 points with nicer shops, restaurants, and bars. Go to the Riverbanks Zoo and Gardens. Widely acclaimed as one of Columbia's best attractions with 4.7 stars on Google. Very quaint Zoo with all the animals you want to see. Takes no more than 1.5 hours to see everything. Ticket Prices. Visit the South Carolina State Museum. Top 10 reasons to visit the South Carolina State Museum. Ticket Prices (Includes entry to 4 floors of permanent and changing exhibits). Visit the South Carolina State House. Free to enter (other than your taxes). State House Portrait and Art Collection The South Carolina State House and grounds of the Capitol Complex are home to many beautiful portraits, monuments, plaques and other works of art. These works honor the many of the people and events that are an important part of the history of South Carolina and the United States.