Government of India forbids any NRI from buying agricutural land in India. If any of your family member lives in India, you can buy agricultural land in his/her name. A resident can buy up to 15 STANDARD acres of wet land. For dry lands, I think it is 30 acres ( I am not sure; but it is more than wet land area). Note, the maximum area one can own in Tamil Nadu is NOT physical area. Standard acre to physical acre conversion factor depends on soil quality, water availability etc. If you need more detail send me PM.
Each state has its own laws for possessing agricultural land.
You can buy commercial property in India.