The Tyrones' summer house is probably based on O'Neill's childhood summer home in New London, Connecticut. The house itself is thematically important because it's the closest thing the characters have to a home, but it really doesn't do the job of providing a emotionally safe, comfortable, haven for the characters.
From the opening stage directions, we can tell that the house is more for show than for function. The front parlor is "rarely occupied" and the back parlor is "never used except as a passage" (1.1.opening stage directions).
Basically, the house doesn't feel lived-in. Mary makes this explicit throughout Act II as she complains about never feeling at home in the house or the neighborhood. In fact, the only part of the house that does feel like it's gotten real use are the books, which O'Neill catalogs exhaustively. For more on those books, see Edmund's "Character Analysis."
So what does it mean that the characters don't have a home? Well, like they say, "Home is where the heart is." Basically, even if the Tyrone family members really do love each other, what they love about each other isn't in the present, but in the past. See the "Memory and The Past" theme for more, but we just want to summarize that the Tyrones find genuine home not in the summer house, but in their respective memories of happier times when they felt comfortable with their lives.
More broadly, we should also note the role played by the weather, the foghorn, and the yacht bells. These aspects of the setting all carry serious symbolic significance, some of which is openly articulated by the characters. See "Symbols, Imagery, Allegory" for an examination of fog as a metaphor for addiction.