In the book Chains by Laurie Halse Anderson, who lived on a big plantation? Who lived on a small farm? And who lived in the city?

Isabel and Ruth lived in all three of those locations.  The large plantation, small farm, and city house all coincide with specific slave owners that Isabel and Ruth worked for.  

Miss Mary Finch owned the small farm.  The reader never gets to meet Miss Mary Finch.  She is already dead by the time the book begins.  Readers do get a sense that she was a decent slave owner though.  Isabel wishes that she could go back and work for Miss Mary Finch, and readers know that she had given Isabel and Ruth their freedom as well.  

Mr. Malbone is the owner of the large plantation.  He is mentioned exactly twice in the novel.  He was Isabel's and Ruth's first owner, and he was forced to sell Isabel and her family because he had too many debts.

They sold all of us from the plantation when old Mister Malbone run up his debts too high.  His bankers wanted their pounds of flesh.  Our flesh. 

The Locktons live in the city.  They are horrible to Isabel and Ruth.  Madam Lockton even goes so far as to brand Isabel's face.  Lady Seymour also lives in the city, and she treats Isabel with decency.