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

If you are looking for corporate jobs, you should go to team lease and adecco. There was another called mafoi, whose name has changed.
Most of the large corporates are taking people from them for the junior / assistant positions in corporate hr. it's probably your best option to get in.
Pune and nashik re also good places. But it depends on your inclination and why you moved from chennai to mumbai