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 http://magento.stackexchange.com/questions/34259/how-add-indian-state


But for ***city you need do some customization by follow*** the like http://magento.stackexchange.com/questions/34259/how-add-indian-state