If user select "INDIA" country in billing step on checkout step then indian state and city should be display in dropdown.
My default country is "USA"
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Magento is saved some countries state list at database table
directory_country_region.Such as like USA,Canada.
For india, state list does not exits in that table So,state is not coming as dropdown at checkout.
So,you need to insert states list of india at Table.In this case,you need follow this link How add indian State?
But for city you need do some customization by follow the like How add indian State?