What is an example of the pursuit of nostalgia in A Streetcar Named Desire?

The most important example of nostalgia in the play is Belle Reve, the Mississippi plantation on which Blanche and Stella grew up. Blanche later reveals to her sister that the property has been lost due to unpaid family debts.

Williams beautifully creates Belle Reve, which translates to English as "Beautiful Dream," as a metaphor for the collapse of the Old South. What is interesting is that he does this without judgment. He does not set up Blanche or Stella as superior remnants of a lost world of manners and chivalry, nor does he look upon the modern, post-war world with relief. 

We are introduced to the plantation through a discussion between Blanche and Stella's downstairs neighbor, Eunice:

Eunice: And you're from Mississippi, huh?

Blanche: Yes.

Eunice: She showed me a picture of your home-place, the plantation.

Blanche: Belle Reve?

Eunice: A great big place with white columns.

Blanche: Yes...

Eunice: A place like that must be awful hard to keep up.

After this last comment from Eunice, Blanche politely excuses herself, claiming exhaustion. The exhaustion is physical, as well as spiritual.

The mental image one gets of Belle Reve might be similar to that of Tara in Gone With the Wind: a large house in Greek Revival style, a symbol of the classical social order of the South -- planter class, commoner, and slave. This social order has been dismantled; but Blanche, still holding on to the memory of what was, is unable to cope.

To save the property, and to survive after being fired from her school district for inappropriate conduct with a male student, she resorts to prostituting herself at The Flamingo Motel. This choice, coupled with her being raped by Stanley, undoes the myth created around her and other Southern white women as "flowers of femininity," or Southern belles, pure and wholesome.

Unlike her sister, Blanche does not fully embrace her sexuality. To do so would require self-awareness and authenticity, and she has neither. Her sense of herself as a Southern aristocrat who truly belongs in "Belle Reve" will not allow her to face the reality of her life in the post-war world.