I have 5 days

Day 1

~3.2 km between stops

1. The Metropolitan Museum of Art
2. Central Park
3. American Museum of Natural History
4. Solomon R. Guggenheim Museum
5. Cooper Hewitt
6. Islamic Cultural Center of New York

Day 2

~6.6 km between stops

1. Museum of the City of New York
2. Conservatory Garden
3. Cathedral of Saint John the Divine
4. Frick Collection
5. Central Park Zoo Security
6. Moma Museum

Day 3

~2 km between stops

1. Top of the Rock
2. Rockefeller Capital Management
3. St. Patrick's Cathedral
4. Chrysler Building
5. Morgan Library & Museum
6. Empire State Building

Day 4

~6.8 km between stops

1. New York Public Library
2. Bryant Park
3. Museum of Arts and Design
4. Riverside Park
5. Intrepid Museum
6. Flatiron Plaza

Day 5

~6.3 km between stops

1. Union Square, Manhattan
2. Washington Square Park
3. New York City Fire Museum
4. Hudson River Park
5. Whitney Museum of American Art
6. Tompkins Square Park