"We live in New York."
Translation:Novi Eboraci habitamus.
Novi Eboraci is the locative case (which is only used by names of cities, towns, small islands, and a handful of other nouns like domus), it itself means 'in New York' and is not used with the preposition in.
The preposition in takes the ablative case when talking about a static location (no movement to or from). Second declension (like Novum Eboracum here) nouns have an -o ending for the ablative as well: in foro -> 'in the forum/market'.