March 13, 2012 -- On her first trip to New York City, Jaycee Dugard attended a star-studded awards ceremony, took in a Broadway play and was awed by the city's skyscrapers. But for her, the most memorable part of the trip was going for pizza. "I've had a great time in New York and it's been amazing. Just an incredible city and so much to do," Dugard told ABC News' Diane Sawyer in an exclusive interview. "Just walking down the street. With everybody. It was my favorite moment."

For a woman who had spent most of her life held captive in the backyard of Philip and Nancy Garrido and who had been reclusive since her rescue to make sure her notoriety did not affect her children, it was liberating not to have to hide.

Dugard says her and her daughters are leading perfectly normal life and that the girls are doing quite well in school. *

Dugard was kidnapped in 1991 when she was 11 years old and held captive for 18 years by the Garridos. She was raped and gave birth to two daughters in captivity before being rescued in 2009. She wrote a bestselling book about her ordeal last year.

Dugard, 31, was in New York City for the Diane von Furstenberg Awards and although she was surrounded by some of the most powerful and influential women in the world at the event it was Dugard who stole the show.

Oprah Winfrey, who was also honored, used part of her speech to tell Dugard, "I am so proud of you, your courage, your ability to press onward toward the future."

Dugard, who received the Inspiration Award, told Sawyer the thing she loves the most every day is freedom. "Just being free to do what I want to do, when I want to do it," she said. "That's the whole learning process to, to know that you can."

Part of enjoying her freedom is making sure the past does not have hold of her, and Dugard told Sawyer that the traumatic ordeal is not on her mind every day and that she decided to forgive Phillip and Nancy Garrido in order to move on with her life.

"It's not with me every day. That is over. Nancy and Philip are behind bars," she said. "There is so much out here to do and feel. … I feel like I can make a difference. … I don't want to be remembered for what happened." Dugard wants to be remembered for the work of her foundation, the JAYC Foundation, which stands for Just Ask Yourself to Care.

The foundation uses animal-assisted therapy, along with other support services to treat families recovering from abduction and the aftermath of traumatic experiences.

Learn more about the JAYC Foundation

Dugard is also trying to make memories, crossing life experiences off a list she made when it seemed freedom was impossible.

So far she has gone on a hot air balloon, learned to drive and regularly rides a horse as part of her therapy, and bragged she has advanced to cantering with her horse and is now saddling the horse by herself. Working with horses, she said, teaches her confidence and assertiveness.

"You have to be very sure of yourself when you're riding. You don't want to have any doubts in your mind because they'll sense that," she said. "I had a little fall, so yeah."

She still wants to see the pyramids, swim with dolphins, touch a whale and take a train ride. And she hopes to write another book.

*This story has been updated to reflect that while leading a very private life Dugard and her family are not in hiding.