I live two blocks from Prospect Park, which Frederick Law Olmsted and Calvert Vaux created in the 1860s to serve a rapidly growing urban population. Even though they designed New York's Central Park and Boston's "Emerald Necklace," Prospect Park is often considered their masterpiece (http://www.prospectpark.org/hist/). I spend a great deal of time there, and I must have walked nearly every trail as well as starting several of my own.
Impressions: Biking aroound the park. The bike lane and jogging lane are always busy, a steady stream of exercising humans all moving in the same direction. In this case, the Other is the one who bikes or rides clockwise. Horseback riders on our left, then past the pond with the ducks and swans and people tossing pieces of bread.
Third Street playground--Modern jungle gyms form the periphery. A sandbox, swings, a water fountain, pigeons, spiral-footed plastic rides. Parents or babysitters or nannies or grandparents with strollers. A racial and ethnic mix.
The Long Meadow is packed on weekends and summer days. Frisbee throwers, volleyball or baseball players, dogs, babies, picnics, birthday parties, sunbathing. Couples lying on blankets or strolling hand-in-hand.

Sledding--Several good hills, but the best for sledding is located near the Pincis House. On Snow Days dozens of people use that hill. Sleek sleds with shiny runners, toboggans, plastic sheets, round boards. The long walk up the hill. The shrieks of joy. Adults running over kids, making them cry. Angry looks from parents.
Carousel--Of the 6,000 carousels constructed in the United States during the golden age of carnivals in the early part of the 20th century, only 200 remain intact. The Prospect Park Carousel is one of them. (http://www.prospectpark.org/hist/main.cfm?target=../dest/caro_hist) I've taken both of my children there, often walking across the park to reach it. Happy memories here. Zack and Lila have outgrown carousels now.
Bandshell--I make sure to go to as many concerts, performances and special events as I can as part of the Celebrate Brooklyn festival every summer. Already this summer I've seen Laurie Anderson and Natalie MacMaster. Other summers I caught The Lincoln Center Jazz Orchestra with Wynton Marsalis, Fritz Lang's Metroplis on a huge screen with Pere Ubu playing live film music, The African Music Festival, Yo La Tengo and Burning Spear.