In what city does Willy Loman live?
Willy Loman lives in New York City. According to the brief paragraph preceding Act One:
The action takes place in Willy Loman's house and yard and in various places he visits in the New York and Boston of today.
In the opening of Act One, Willy has returned home. He tells his wife that he wasn't able to make it past Yonkers.
I suddenly couldn't drive any more. The car kept going of onto the shoulder, y'know?
Yonkers is a suburb of New York. It is only about two miles north of the northernmost past of Manhattan. Willy was just starting on a business trip to cover his New England territory. The fact that he was still in New York City shows that this is where he lives. He is obviously getting too old to continue covering such and extensive territory as Maine, Vermont, New Hampshire, Massachusetts, Connecticut and Rhode Island, which make up New England; but when he asks to be transferred to a territory closer to home, it leads to an argument with his boss that results in his getting fired.
Willy's little house has changed in the years he and his wife Linda have lived there and raised their two sons, Biff and Happy. It is surrounded by tall buildings that cut off much of the sunlight. Willy tells Linda:
There's not a breath of fresh air in the neighborhood. The grass don't grow any more, you can't raise a carrot in the back yard. They shouldn't have a law against apartment houses.