I was living in PA when I applied, so I wound up putting my home address (and not my parent's address in FL) on the application. I was hoping the Northeast bias would help me get some interviews from schools up there (which it did). On the other hand, I also wanted to get back to Florida where all my family and friends were, so mid-way through the application cycle (after sending in secondaries and hearing nothing back from the FL schools) I sent a few letters of interest to the schools in FL. In the letters I basically told them I was from the area, maintained strong ties to the area, and had a "strong desire to give back to the community that raised me" (or something like that). Two weeks after I sent the letters I received an invitation to interview.
I wouldn't recommend doing it the way I did as your first option, but if you can't claim to be a resident of a specific state on your application for whatever reason, there's always the option of letting them know your ties to the area through a letter of interest or something.
And yea, to answer your question, it'll definitely help your chances if you let them know you want to stay in the region, and it'll help even more so if you can prove that you have ties to the region as well.
