Learn Spanish (Latin America): ¡La lluvia nunca para en esta ciudad!

You are right that para is a very common word meaning "for." But in this sentence, it is actually a verb! It is the "it" form of the verb parar, which means "to stop." So, la lluvia nunca para translates to "the rain never stops."

Could I put nunca after the verb instead?

Yes, but you would need to use a double negative. In Spanish, if a negative word like nunca (never) comes after the verb, you must put no before the verb. You could perfectly say: ¡La lluvia no para nunca en esta ciudad!

Why is it esta ciudad instead of este ciudad?

Even though it doesn't end in an "-a", ciudad is a feminine noun. Therefore, it needs the feminine word for "this", which is esta. As a helpful rule, almost all Spanish nouns ending in "-dad" (like universidad or verdad) are feminine.

I sometimes see esta written with an accent (está). Why doesn't it have one here?