The Day After Tomorrow

Paleoclimatologist Jack Hall and his colleagues, Frank and Jason, are drilling for ice-core samples on the Larsen Ice Shelf for NOAA when the shelf breaks off. When Jack later presents his findings on global warming at a United Nations conference in New Delhi, he fails to convince diplomats or U.S. Vice President Raymond Becker. However, Professor Terry Rapson of the Hedland Climate Research Centre in Scotland believes Jack's theories. Several buoys in the North Atlantic simultaneously register a sharp drop in water temperature, and Rapson concludes that melting polar ice has begun to disrupt the North Atlantic Current. He contacts Jack, whose paleoclimatologic weather model demonstrates how climate changes caused the first ice age. His team, including NASA meteorologist Janet Tokada, builds a forecast model based on Jack's findings.
Around the world, violent weather causes widespread destruction; U.S. President Blake authorizes the FAA to halt air traffic due to severe turbulence. On the International Space Station, three astronauts see a storm system spanning the Northern Hemisphere which soon develops into three hurricane-like superstorms. The temperature of the eyes of the storms is â150Â Â°F (â101Â Â°C), instantly freezing anything in their paths. The cells, located over Canada, Scotland, and Siberia, will affect all of their respective continents within days. During this time, tornadoes destroy Los Angeles.
In Manhattan, Jack's son Sam learns about the worsening weather when he participates in an academic decathlon. Although Sam promises to be on the next train home, flooding quickly closes the subway and Grand Central Terminal as a storm surge strikes New York City. Sam and a large group of people seek shelter in the New York Public Library and his teammate, Laura Chapman, accidentally cuts her leg. In Scotland, Rapson and his colleagues at the Hedland Centre die in the European superstorm.
As suggested by Jack, President Blake orders the evacuation of the southern United States (with most refugees heading for Mexico) and warns the northern half of the country to seek shelter. Jack and his team set out for Manhattan to find Sam; when their truck crashes north of Philadelphia, the group continues on snowshoes. En route, Frank falls through the glass roof of a snow-covered shopping mall. As Jason and Jack try to pull him up, the glass under them continues cracking; Frank sacrifices himself by cutting the rope. Most of the group sheltered in the library leave (despite Sam's warning) when the water outside freezes, leaving Sam, his friends, and a few others who trust him. They burn books to stay warm, and break into a vending machine for food. Sam admits his feelings for Laura (who has apparently caught a cold), and she reciprocates. At the U.S. refugee camp in Mexico, Becker learns that Blake died when his motorcade was enveloped by the superstorm and he is now the president.
The next morning, Sam's group determines that Laura has blood poisoning from the cut on her leg. Sam and two others search for penicillin in a derelict Russian cargo ship which drifted inland. Although they find food and supplies, they also encounter a pack of escaped wolves from a city zoo. The eye of the North American superstorm passes over the city, freezing it solid, and the three barely return to the library in time. Jack, also in the eye with an unconscious Jason, narrowly escapes the freeze himself in an abandoned restaurant.
Days later, as the superstorms dissipate, Jack and Jason reach New York City and find Sam's group alive. They radio the news to the U.S. government in exile in Mexico, and Becker orders rescue teams to search for other survivors in the northern states in his first address as president. On the ISS, astronauts look down in amazement at an Earth whose northern hemisphere is mostly covered by ice and snow.

Question: Where does Sam seek shelter?
Answer: New York Public Library