Where do law students who come from other cities to intern at offices in Lower Parel or Nariman Point stay?
Is there any place to stay which will be within, say, 30k?

30K a month can get you the world. There are several nice PGs you'll find in Lower Parel, Worli, Byculla, Crawford Market etc. Ask your college seniors or get in touch with a broker

Do they give it for rent for 4 weeks?

BUMP.
Also, do consider living in Bandra. Travel will be there. But you can save on rent.

Bump

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We used to stay at Seva Niketan (Men’s hostel) in Byculla. Some of us also used to stay in Wilson College Hostel. But this was in 2007 - 2008.