"My sons live in Rome."
Translation:Filii mei Romae habitant.
Romae in the given sentence is the locative case (specifying location), the in is implied with the locative. The locative only occurs with names of cities, towns, small islands and a handful of other special nouns (like domus).
Since our subject is plural ('my sons') we cannot use habitat since that is the singular third person. Habitant is the third person plural.