1. Go to Central Park - it is one of the largest and most beautiful parks I've ever seen.
2. Just walk around, buy street food, and take the subway - New York is such an awesome place that you'll find lots of interesting things.
3. Go to Times Square (it's awesome!)
4. Go to New York's Chinatown - I've been there, and you can find really cool stuff and really unique and delicious food.
5. Visit the Brooklyn Botanical Garden - it's free Tuesdays.
6. Go to 5th Avenue - it has tons of cool architecture and stores
8.5th Avenue includes the world's only NBA store. The NBA store includes a half court where your little sister can test out her basketball skills!
7.If you go to 5th Avenue, I would also at least take a look at the architecture of the Solomon R. Guggenheim Museum since it's really unique and cool. It costs to go in it, but the architecture is amazing on its own. The famous Frank Lloyd Wright designed it.
8. Some other architecturally amazing buildings are the Empire State Building, the Grand Central Terminal, the Rockefeller Center, and the Seagram Building
9. Visit the Sony Wonder Technology Lab. It has free admission, and I think your little sister would love it!
10. New York's amazing and often gigantic cathedrals are also fun to visit. Some good ones are the Cathedral Church of St. John the Divine, the Riverside Church (has the world's highest carillion tower at 400 ft), and the Gothic St. Patrick's Cathedral (also on 5th Avenue)
11. The New York Public Library is also amazing
12. Take a cruise on the Staten Island Ferry (it's free) - you'll be able to see the Statue of Liberty from it!
13. Walk across the Brooklyn Bridge's footpath. The view is amazing! Then you can walk along the Brooklyn Heights Promenade.
Hope that helps!
I've been to NYC a bunch of times