Unemployed - Wait For A Core HR Role Or Join A Recruitment Consultancy?

If you are looking for corporate jobs, you should go to TeamLease and Adecco. There was another called Mafoi, whose name has changed. Most of the large corporates are hiring people from them for junior/assistant positions in corporate HR. It's probably your best option to get in.

Pune and Nashik are also good places. But it depends on your inclination and why you moved from Chennai to Mumbai.