Try using Python's built-in dir(theobject) method to inspect CountryInfo object like so:
dir(CountryInfo)
In order to list all the fields and methods of your object (as a tuple) and the inspect module (as codeape write) to list the fields and methods within the doc. Or use help(object) to get details of the object whether there exist a method for finding cities given a state.
From the results, you will be able to know if you can get your cities or not from the countryinfo module.
I saw a resource about this module here: https://medium.com/analytics-vidhya/fetch-all-information-of-any-country-using-python-baa72a669d68
However, it only gives you the capital city for a given country.
data2 = country.capital()
print(data2)
#Output:
New Delhi
You might need a different python module.
Checkout Retrieve cities list of a country