As salaamualaikum wa rahmatullilahi wabarkaatahu Sheikh:
I work in a different city than where my family is. My work is 250 kilometers from my family (parents, and brothers). I work from Monday to Friday and return to my family for Saturday and Sunday. I have an apartment where I work. My question is can I shorten my salaat in my working city or are both cities considered to be my home?
Your home town, the one where your family lives, is your home. The town which you intend to stay in for more than four days is also considered a place of residence, according to the opinion of the majority of scholars. Therefore you are not allowed to enjoy the concessions of the traveler (i.e. shortening and combining the prayers) in either place. However, you can shorten and combine prayers while traveling in between the two places.
Refer to questions under Salaat Ul-Musaafir (Prayer of the Traveler).