A teenage girl named Eva (Eszter Balint) has arrived from Hungary standing outside an airfield full of airplanes coming and going not sure where to go and about to move forward.
A single, self-centered, and unemployed young hipster slacker named Willie (John Lurie), who has lived in America for over 10 years abandoning his Hungarian roots and insistent on speaking only English, lives in a simple one room apartment on Manhattan's lower east side and answers a telephone with his Hungarian aunt Lottie telling him he has a niece of his arriving to visit him and stay for a short time. He's annoyed that it will disrupt his otherwise private life. She has to go into the hospital for 10 days and Eva will have to delay her visit on seeing her until then and stay with Willie.
The young lady, Eva, is walking to Willie's apartment on the lower east side and we get glimpses of a lonely, desolate landscape of a part of Manhattan few are familiar with as she walks down the street playing Screamin' Jay Hawkins on a tape recorder singing "I've Got a Spell on You"
Eva arrives at Willie's apartment and he's not all that thrilled about her visitation disrupting his otherwise monotonous and lonely lifestyle. He lets her in and gives her a place to sleep. During this timeframe, Willie does little besides watch TV, sleep, introduce her to TV dinners, play solitaire, and introduce her to his friend Eddie, a fellow friend. During this timeframe, little happens, but the two bond together and he accepts her as family.
After staying with Willie over a week, Eva leaves to board a train to Cleveland, where her Aunt Lottie lives. Eddie comes to say goodbye to her on the street after she leaves Willie's apartment changing out of a tacky dress he bought her. Eddie then goes to Willie's apartment and the two of them have a beer together with no conversation.
A year later, Eddie and Willie are having a poker game at a man's apartment and they win over $600 with one man outraged that they cheated, but they walk out with the loot and intend to travel with it.
Soon afterwards, Eddie and Willie borrow an old 1965 Plymouth out of New York City bound for Cleveland to see Eva. During the trip, little happens except Willie annoying Eddie from time to time trying to have conversation with him and both of them realizing the weather is just getting colder.
Willie and Eddie arrive in Cleveland at his Aunt Lottie's modest house in a lonely industrial section. Lottie is a feisty and witty elderly woman that welcomes them to her home feeding them a hearty meal of goulash and bread before they pick Eva up from work.
Willie and Eddie pay a surprise visit to Eva at the hot dog stand she works at and pick her up from work. Eddie is delighted he was remembered.
Some time later, the trio are living monotonously at Aunt Lottie's home still bored at not doing anything, but Eva invites them to a Kung Fu movie with a boyfriend that they're not impressed with. And the four of them are bored with the movie.
Still bored with their visit, the trio are challenging Aunt Lottie to a card game she keeps winning and they go to see Lake Erie. Willie and Eddie are fed up with the cold and boredom and decide to take off back to New York City. They are frustrated and want to pick up Eva and go to Florida. They go back to take Eva, despite Aunt Lottie's protests. She opposes them endlessly in Hungarian after they pick up Eva and she calls them "a son of a bitch".
Soon after arriving in Florida, they don't find it any more thrilling and they stay at a lonely motel
Willie and Eddie end up losing most of their money on dog races. At this point, they decide to go back and bet on horse races. Willie refuses to let Eva come along, so she goes out on the beach for a walk.
Eva ends up being mistaken by a drug dealer, and is given a large sum of money. Right after being given the money, a woman dressed almost identical to her shows up with nobody around.
Eva goes back to the motel, leaves some of the money for Willie and Eddie, and writes them a note explaining that she is going to the airport, and then goes there. When she arrives, she discovers that the only flight to Europe left that day is to Budapest, which is where she originally came from. She decides to wait until the following day, and goes back to the motel. Willie and Eddie end up winning all of their money back at the horse races. But when they get back, Eva is gone, and Willie reads her note and they go to the airport to stop her from leaving. When they get there, Willie conceives a plan: buy a ticket, get on the plane, find Eva and convince her to stay in the states. What Willie didn't know was that at the time Eva made her decision about flying back to Budapest, there was only one free seat left on the plane. The second to last shot shows Eddie outside watching the plane leave, and he realizes what has happened. The final shot shows Eva back at the motel, returning to an empty room.