None of these seven needs a bus or a car. The subway runs 24 hours a day and reaches every one of them, so a metro card and a little walking cover the whole list.
The Statue of Liberty and Ellis Island
The statue and the old immigration halls stand in the harbor rather than on the street grid, so they arrive as one trip, and the ride out gives you the Manhattan skyline from the water. Allow half a day for the pair, and take the crossing in summer as a way off the hot sidewalks.

Check the ferry operator's timetable and ticket rules for your own date, then plan it as a morning. It suits families traveling with children, because a boat holds attention at any age.
Times Square
Times Square costs nothing and takes almost no planning. Walk it once after dark, take your photographs, and an hour covers it. Stay alert in the crowds while you are here, and the same way around Grand Central Station, where the two biggest crowds of the week both sit.

Keep to the lit blocks, keep your group together, and it works in any month. It suits a first evening, before you have worked out the subway.
The Broadway Theater District
The theater district belongs to the evening, and it is the one city pick worth arranging before you leave home. New productions open in May and October, so if your dates land in those months, sort the tickets before you book flights.
One show is enough for a first trip; an evening in a theater is a long evening. It suits couples and families with older children who can sit through a full performance.
Central Park
Central Park is free, walkable from Midtown, and it changes character with the season. October is when the foliage turns red, orange and gold, and the park fills half a day in any month: cherry blossom in spring, Shakespeare in the Park and the SummerStage concerts in summer, snow and empty paths in winter.

Take a map or keep your phone charged, because the paths do not run straight. It suits families, walkers and anyone who has spent two days on hard pavement.
The Empire State Building
The observation deck is the view of New York most first-timers picture. Give it an hour up there, and check the opening hours and ticket options before you go, because both move through the year. The deck is busiest in the sticky afternoons of July and August, when the city runs into the mid-80s°F and the day often closes with a thunderstorm, so a morning slot is the easier one.

If you would rather see the skyline from the air, helicopter tours fly out of the city for 15 to 20 minutes, in a different price bracket. On the ground, the deck is a good pick for the last morning of a city stay.
Rockefeller Center
Rockefeller Center earns its place on the list in winter, for three things: the Christmas tree lighting, the Radio City Christmas Spectacular, and ice skating at Rockefeller Center or Bryant Park's Winter Village.

Outside the winter months, it is a short walk and a look at the buildings rather than a stop of its own, and the same visit pairs neatly with a theater evening. Lunar New Year celebrations and the city's Restaurant Week menus give January and February a second reason to come, with prix-fixe deals at restaurants around town. It suits anyone traveling between December and February.
The September 11 Memorial & Museum
This pick asks for time rather than money. Give it two to three hours and treat it as a half day once you add the walk there and back. It is also the one stop where you should check opening days and entry rules for your own date instead of assuming them.
It suits adults and older children more than very young ones.