Chicago architect Sam Baldwin loses his wife Maggie to cancer. He and his eight-year-old son Jonah start anew in Seattle, Washington, but Sam continues to grieve. A year and a half later, on Christmas Eve 1992, Jonahâwho wants his father to find a new wifeâcalls in to a radio talk show. Jonah persuades a reluctant Sam to go on the air to talk about how much he misses Maggie. Hundreds of women from around the country who hear the program and are touched by the story write to Sam. One of the listeners is Annie Reed, a Baltimore Sun reporter. She is engaged to amiable, suitable Walter but feels there is something missing from their cordial relationship, feeling no "magic". After watching the film An Affair to Remember, Annie impulsively writes a letter suggesting that Sam meet her on top of the Empire State Building on Valentine's Day. She does not intend to mail it, but her friend and editor Becky does it for her and agrees to send Annie to Seattle to "look into doing a story on those radio shows."
Sam begins dating a co-worker Victoria, whom Jonah dislikes. Jonah, a baseball fan, reads Annie's letter and likes that it mentions the Baltimore Orioles, but he fails to convince his father to go to New York to meet Annie. On the advice of his playmate Jessica, Jonah replies to Annie, agreeing to the New York meeting. While dropping Victoria off at the airport for a flight, Sam sees Annie exiting from her plane and is mesmerized by her, although he has no idea who she is. Annie later secretly watches Sam and Jonah playing on the beach together but mistakes Sam's sister for his girlfriend. He recognizes her from the airport and says "Hello," but Annie can only respond with another "Hello" before fleeing. She decides she is being foolish and goes to New York to meet Walter for Valentine's Day.
With Jessica's help, Jonah flies to New York without Sam's permission and goes to the Empire State Building searching for Annie. Distraught, Sam follows Jonah and finds him on the observation deck. Meanwhile, Annie sees the skyscraper from the Rainbow Room where she is dining with Walter and confesses her doubts to him, amicably ending their engagement. She rushes to the Empire State Building but is told that the observation deck is closed before the guard lets her go. She arrives at the top just moments after the doors to the down elevator close with Sam and Jonah inside.
In spite of the observation deck being deserted, Annie discovers a backpack that Jonah left behind. As she pulls out Jonah's teddy bear from the backpack, Sam and Jonah emerge from the elevator, and the three meet for the first time. On the advice of the elevator operator, Sam indicates they should go, momentarily making it unclear what his intentions are, and offers his hand to Annie. "Magic" is implied, because the couple keep holding hands as the three enter the elevator together. When the elevator door closes, the last thing we see is Jonah's beaming smile as he realizes his and Jessica's plan to bring Annie and his father together has worked.

Question: Why did Sam finally go to the Empire State Building?
Answer: To find Jonah
Alternative answer: Because Jonah went without his permission.