VLSI has become one of the most preferred branches of the ECE department. Its placements are similar across all the top IITs with the top recruiters being Intel, Qualcomm, Texas Instruments, Cadence, Synopsis, Analog Devices, TSMC, etc.
However, the difference lies in the quality of professors and their respective expertise. A few IITs with their area of specialization are as follows
If placements are your only concern, I will suggest you go for IIT KGP which usually enjoys 100% placements with an average package of around INR 17 LPA.