I have noticed that people often move from the place where they are reading their Farz namaaz to another place in the mosque to read their sunnat and nafl salaah. Is there some benefits in doing this?

It is Mustahabb (preferable) to break up the Sufoof (rows) and spread out
after the Fardh Salaat so that a person entering does not fall into doubt
regarding the Jamaat's completion.

Concerning a Munfarid (person who performed his Fardh without Jamaat), it
will be better for him to shift to another place for his Sunnat and Nafl
Salaats as well. (Fataawa Darul Uloom vol.1 pg.243; Darul Ishaat)

and Allah Ta'ala Knows Best

Mufti Ebrahim Desai
FATWA DEPT.