"She studies in New York."
Translation:Ea Novi Eboraci studet.
The case is different, the case being the use/function in the sentence.
Here, Novi Eboraci is the locative case, specifying where something happens or is located. Her studying takes place in New York. Note, however, that the locative is only available for cities, towns, small islands, and a few other nouns (such as domus). Novi Eboraci can also be the genitive form.
Novum Eboracum is the nominative, accusative, and vocative form.
The nominative would be used if New York was the subject of the sentence, like in the sentence: New York has streets. -> Novum Eboracum vias habet.
The accusative would usually be used as the direct object, like in the sentence: I love New York. -> Novum Eboracum amo.
The vocative is used for direct address, like in: Hello New York! -> Ave Novum Eboracum!