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10km from Lower Parel includes Cuffe Parade, Bandra West, Mahim, Bandra East, and Dharavi. So the rent range will vary quite significantly depending on where you want to stay.

You'll have to take a call what you want to prioritise but at 50k for a 2bhk, you won't find a 2bhk in the nicer part of town or in the fancier buildings (think buildings with gyms, swimming pool, etc.). There isn't any one specific place where law firm people stay - you will find what you prioritise may be quite different from what someone else might. I personally started prioritising staying close to office (almost) above all else after a few years but I know people who didn't mind spending 1+ hour travelling back and forth since they liked living in Bandra West or Juhu.

I find a lot of people don't count the taxi fare to and from office when considering the "total all-in cost". It is for this reason I find staying in Bhakti Park to not make a lot of sense. That being said, I took the local trains for many years and don't let anyone convince you that trains aren't a perfectly decent way to travel to work. To make local trains a sensible option, try to not stay too far away from your starting local station and ideally stay near a place where you get taxis / autos quickly. LP / Elphinstone Road local stations are a walking distance (
Reasonably priced area, should you be willing to travel by the local trains, would be Sion / Chunabhatti. It will not be as lively as the Western Suburbs, but you can get semi furnished 1 BHK's for a reasonable rent in those areas. On the Central Line, you have to get off at Parel (it shares a station with Elphinstone Road/Prabhadevi on the Western Line), from where most LP law firms are at a walking distance. Else, if you are ok with 1 RK apartments, search in Prabhadevi, Naigaon in Dadar East, Shivaji Park, Lalbaug (be ready to bear with a lot of noise during Ganesh Chaturthi if you are staying in Lalbaug, Currey Road and Chinchpokli). Also look at a few old buildings in both Parel and Lower Parel. If you are willing to commute by local trains, you will get decent semi furnished and even fully furnished apartments in Vikhroli and Mulund on the Central Line, as well as Borivali and Goregaon on the Western Line.
Maybe try looking for a flat in areas like Parel, Dadar, etc. Parel is a good option as the rents are still in the range of 20k while being super close to the offices in Lower Parel and other fun amenities.