"The family lives in Philadelphia."
Translation:Familia Philadelphiae habitat.
"Familia" was originally the group of slaves in a house, property of the father ("paterfamilias") ... "Familia", with the meaning of group of relatives (father, mother, sons...) used to be known as "propinqui, cognati (in plural)". Anyway, the sense was changing through time. I do not pretend to correct anything. This is just a comment.
The names of cities/towns and small islands, as well as a small handful of words (rus, domus, humus) use the locative without any preposition. All else take "in" plus the ablative case.
Here is a plain-English overview of what the cases are and how they work:
Latin cases, in English
Adjectives must agree in gender, number, and case with the nouns they modify, but they have their own declensions. Sometimes you get lucky and the adjective just happens to follow the same declension as the noun, but that is not a guarantee.