There are a few small VLSI companies in Mumbai.
Powai Lab (in IIT mumbai Campus): basically working in EDA Tool Development
iFlect Technologies IPL
System Automation Group
infinity
may be some more...
1. Netlogic (most of the work is into asic verification)
2. patni computers (FPGA design/verificatiion )
3. Transasia biomedicals (biomedical instruments domain.)
But in my opinion Mumbai is not the right place for a VLSI techie.