Learn Russian: Спустя час картограф нашёл город Москву на этом большом глобусе. - An hour later, the cartographer found the city of Moscow on this big globe.

This highlights appositive agreement. In standard Russian, familiar geographical names (like well-known cities or rivers) agree in case with the generic noun describing them. Because the cartographer found the city (direct object, accusative город), the name Москва changes to match it, becoming Москву.

Is it ever grammatically correct to leave the city name in the nominative and say нашёл город Москва?

Yes, but mostly in very formal, military, or bureaucratic contexts. In official documents, the proper name often stays in the nominative to avoid any confusion about a town's exact exact spelling or name. In standard literature and everyday speech, however, matching the cases is the expected choice for familiar places.

What case is час in the phrase спустя час?

It is in the accusative case. The preposition спустя (meaning "after" or "later") always takes the accusative. Since час is an inanimate masculine noun, its accusative form looks exactly like its nominative. You can also reverse the word order to час спустя for a slightly more literary feel.

Could I use через час instead of спустя час in this sentence?

Yes, in a past-tense narrative like this, both mean "an hour later" and are interchangeable. The difference is that спустя strictly emphasizes an elapsed period of time looking back, while через is more versatile and can also mean "in an hour" when talking about the future.