What is the name of the festival celebrating the arts in NYC during the summer?

The festival that celebrates the arts in New York City during the summer is known as SummerStage. This popular festival features a variety of performances, including music, dance, and theater, held in parks throughout the city, particularly in Central Park. SummerStage provides a platform for both emerging and established artists, enhancing the cultural landscape of New York City during the warmer months.

The other options, while significant events in New York City's cultural calendar, do not specifically focus on a broad celebration of the arts throughout the entire summer. The New York Film Festival primarily showcases films in the fall, Shakespeare in the Park offers theatrical performances of Shakespeare's works typically during the summer months but is a more niche event, and Warm Up is a series of events focused on music and dance at MoMA PS1 but does not encompass the wider arts experience represented by SummerStage. SummerStage stands out as a comprehensive celebration of the arts, making it the correct answer in this context.