I know Linda's dream is to have a close family and Willy's is to live the American dream. But what are Biff's and Happy's dreams?
Biff and Happy are very different brothers, and their life experiences have led them to want things for themselves that are quite dissonant from what their father had primarily wished.
For example, in Act One, Biff confesses how he loves nature, the outdoors, and to feel free. The idea to go to Bill Oliver to get a loan of ten thousand dollars is primarily to get a ranch, raise cattle and fulfill his dream of working at doing what he loves.
Happy is actually more like Willy than Biff is: Happy is the eternal dreamer, shallow, superficial, and entirely devoted to building his own ego. We know that Happy has made it in his own way: he is the one who lives in an apartment, makes his own money, dates extensively, and loves to "ruin" girls so that they would run after him. Either way, Happy is very unsettled still: he says first that he wants to go out West with Biff to help with a ranch as "The Loman Brothers". Then he changes his mind and says that he is waiting for the merchandise manager to die so that he can take over his position. Then he talks about selling sporting goods with Biff, again, as "The Loman Brothers". It seems that Happy, like Willy, becomes fixated on the superficial and "showy", such as the name or title of something. The rest, to them, is unimportant.
At the end, the dreams change one more time. With Willy's death comes a rearrangement of priorities. Here we see who is who. Happy, is willing to continue Willy's dream.
HAPPY: I'm staying right here in this city, and I'm gonna beat this racket. He looks at Biff: The Loman Brothers!
Meanwhile, Biff is obviously not going to follow any of Willy's dreams. In fact, he is going to walk away from it all.
BIFF with a hopeless glance at Happy, bends toward his mother: Let's go, Mom.
Therefore, we can almost predict what will happen next: Happy will continue to perpetuate the fantasy world of Willy Loman, which is what Willy may have or have not wanted. Biff is simply leaving, and walking away from it altogether. We never really get to know.