3 to 5 days in New York with a pass
Four to five days is the sweet spot for a first visit to New York, and the nine-day CityPASS fits it perfectly. The trick is geography: two paid attractions a day in the same neighborhood, with the free city in between.
Day by day: five pass picks, the rest free
CityPASS covers five attractions, so this plan uses exactly five, one or two a day, and fills the gaps with free sights. Day 1, Downtown: the first Statue of Liberty ferry from Battery Park (pick 1; grounds, museum and Ellis Island take 4 to 5 hours), then the 9/11 Museum (pick 2) and the free memorial pools outside it, and sunset on the Brooklyn Bridge walkway (free). Day 2, Midtown West: the Intrepid Museum (pick 3), then a free evening in Times Square and Bryant Park. Day 3, Uptown: the American Museum of Natural History when it opens (pick 4), then a long walk across Central Park (free). Day 4, Midtown: the Empire State Building (pick 5) in the morning, Grand Central and the New York Public Library in between (both free), and back up the Empire State after dark with the same AM/PM ticket. Day 5, West Side: no pass attraction at all: the High Line from Gansevoort Street to Hudson Yards, Chelsea Market and the Hudson River piers, all free.
Want different picks? Swap like for like within the same day: Top of the Rock or Edge for the Empire State Building, the Circle Line for the Intrepid (their piers are next to each other), the Guggenheim for Natural History, or the Whitney for the High Line day. Any sixth paid attraction is a separate ticket.

Three days only?
Keep Days 1, 3 and 4: that is four pass attractions (Statue ferry, 9/11 Museum, Natural History, Empire State). The C3 pass plus a single ticket for the fourth costs about the same as the full pass ($109 plus $31 to $50, against $149), so the full CityPASS is the simpler buy and leaves you a spare pick. If you will only manage three, drop the 9/11 Museum and take C3. Staying longer? The Go City Explorer gives you 30 days, and the nine-day CityPASS still leaves slack for rest days.
What it costs
Is $2,000 enough for five days? For one person, usually yes, if accommodation is paid separately or shared. A realistic daily budget outside the hotel: $60 to $120 for food, $3 a subway ride capped at $35 for seven days, and about $30 a day for sightseeing when a $149 pass is spread over five days. Hotels are the variable: Manhattan rooms rarely drop below $200 a night in peak season, so a solo traveler paying for a room alone will find $2,000 tight. See plan your trip for getting around and free museum times.