I'm trying to describe a country that isn't divided up into anything so distinct as states, or anything terribly specialized, but is divided for the purposes of government, etc. "Quarter" is out because it makes me feel like there can only be four of them, even if that isn't true. "District" is out because, frankly, the Hunger Games has colored the meaning of that term for quite a lot of people. "Region" sounds too open and nebulous. "Sector" sounds too space-stationy.
You could try the word "province":
an administrative division or unit of a country.
Also: "realm" and "domain".
County, shire, range, division, territory, parish, march, zone, partition, ward, constituency, tract, suzerainty, borough, vale, colony, riding, municipality, realm, duchy, fiefdom or earldom.
Though the last few are rather more dependent on the governance than most of the others
How about these:
Another possibility would be canton.
Also consider department ("A territorial division; a district; esp., in France, one of the districts composed of several arrondissements into which the country is divided for governmental purposes; as, the Department of the Loire" and "A military subdivision of a country; as, the Department of the Potomac"), and arrondissement ("An administrative division in some French- or Dutch-speaking countries" and "(Canada) A borough, a submunicipal administrative division") (and division and borough too).
You could try the word county.
I see I'm rather late to this but, especially since we're referring to divisions for governance, I would suggest municipality, especially if it is the lowest level of local government.
Certain terms are speicific to certain geographies at certain times.
Province and provincial are generic terms used in government lingo as an administrative division.
If your context relates to a hypothetical place in an undefined time period, I would suggest a neutral word like province.
Canton is used in ?some geographies ('deliciously swiss', china, other mostly non-English-speaking countries...) and so may not suit a wider native-English-speaking readership.