Junior Year Strategy Session

So I've asked similar questions recently but they've been separate so I'm going to ask this all at once.

I'm ending my sophomore year this semester. I'm currently wrapping up a small PE/VC internship that has been an amazing experience (I was offered to stay on board until graduation but I need to focus on recruitment/school). I've spoken with a few BB banks about recruiting next year and what not.

I also go to college in Manhattan (NYU). i'm assuming then, all the recruiting done here is for jobs in NYC? I am totally cool with interning in NYC between my junior and senior summer, but I WANT to move back to LA upon graduation.

I'm afraid if I articulate off the bat I want to move back to LA upon graduation, I could screw myself out of a summer internship that would help me get a FT offer somewhere in LA - or is that even possible?

I have tons of contacts that i've collected that will be used during the fall semester to recruit. How should I approach my desire to work in LA? Should I even mention it? How would you go about this situation? Should I let HR know that I'm also interested in working in LA and would love to communicate with HR in LA to apply for interviews/superdays?

Lastly, when is a good time to pull out the guns (email addresses, phone numbers, ect) and send my resume/CV? Right at the beginning of fall semester, or is there a specific month/period where I should begin?