"This area is important for our city."
Translation:Ten obszar jest ważny dla naszego miasta.
miasta - here it is genitive case. ( plural nominative=accusative look the same). Genitive could be used for various reasons, here is is because of preposition "dla"
mieście - is locative case. It is used after certain prepositions. Most common are o=about and w=in (when talking about location).