Neuroscience is the current hot cake and it attracts people from almost all disciplines like math, physics, biological sciences, philosophy, engineering, medicine etc.

It covers a broad range of areas like
Neurophysiology
Neurochemistry
Biophysics
Molecular and human genetics
Biostatistics
Computational neuroscience

INSTITUTES IN INDIA

NATIONAL INSTITUTE OF MENTAL HEALTH AND NEURO SCIENCES

National Brain Research Centre, Manesar, Gurgaon Dist, Haryana

Home  NCBS

Centre for Neuroscience -Indian Institute of Science(IISc)

Go through departments and research publication section. A good majority of labs have their own page where all information is stored

Best would be IISC BANGLORE!
And for further information you can go to the below given link:
UG in Neuroscience
-cheers :)