How would I say something on a city level in comparison to a provincial level or national level?
Elections are held nationally every four years, and _________ every two years.
A city, viewed as a governmental and political entity, is called a municipality (see Merriam-Webster), with corresponding adjective municipal and adverb municipally. For example, we often speak of "municipal elections".
However, I must say that the sentence "elections are held municipally every two years" does not sound anywhere near as good to me as the sentence "elections are held nationally every four years"; I don't know why. So I'd suggest instead:
National elections are held every four years, and municipal elections every two years.
Alternatively, in your example, you can use the phrase at the city level:
Elections are held nationally every four years, and at the city level every two years.
"municipal" is the word you're looking for.
Elections are held nationally every four years, and municipally every two years.
- municipal (adj) "of or relating to the government of a city or town"
e.g. Both national and municipal elections are held every four years in this country.
In some English speaking countries, mainly in the US, the term "local elections" is used more often than "municipal elections". See ngram
Another option you might use is "citywide":
- occurring throughout a city; including an entire city: "citywide school board elections."
- open to including, or affecting all the inhabitants of or groups in a city: "a citywide track meet."
"An election where the ballot has choices for the city government (elected officials, proposed ordinances, bond issues, etc). "
As other answers have pointed out, 'municipal' certainly works as the adjective in this case.
However, 'city' itself can also be used (and, at least in the U.S., is frequently used) as the adjective.
For example, all of the following are perfectly normal usages:
At least in the case of the U.S., I would guess that just using 'city' as an attributive noun is more common than 'municipal,' though both are used frequently and the latter is probably considered more formal.