I think it's great that you're looking ahead! You definitely have so much going for you! Although I went to school in NY, I'm actually from CA and ended up moving back so I know how it feels to make that out of state transition. I searched for jobs in most states but mainly stuck with CA. I will try to answer these questions to the best of my ability though:
1. Should I take the NCLEX in New York and get my license through NYS?
Before you either take the NCLEX in New York or Mississippi, I would first take a look and see how long it takes for their State Boards to endorse an RN license. In New York, the endorsement process takes up to 8-10 weeks. Even though they have received your application, they will not process it until you have hit the 8 wk mark (lame, I know). I only recently got my license endorsed but it took me 9 weeks. I was told that it could have taken much longer though because they were still processing applications from a month out. If you had the option, you could take the NCLEX in New York, and then endorse your license in Mississippi (if the wait time is less) and obtain 2 licenses within a shorter period of time.
2. Should I take the NCLEX in Mississippi and work here for a while before I move? I'm not willing to stay longer than 1-2 years before I move.
This is a great option. If you are willing to stay for a couple of years, I think that this would definitely ensure that you got experience under your belt and give you better job options. I understand that this is a tough decision though when you want to move back to NY. Plus, you have already been accepted into an RN-MSN program there (by the way, congratulations!). The job market is tough in NY but definitely trust your gut on this one. The decision comes down to what you think is best for you.
3. Will graduating from a Mississippi school look bad on job applications to NY employers?
It shouldn't look bad. When I applied to CA hospitals with a New York school, sure, they didn't really recognize the school and where I did my clinicals, but they were more concerned with my experiences and the units I had my clinicals on.
4. Would acceptance into a BSN or MSN program at a New York school increase my chances of getting a job in New York?
I think it would, personally. When I applied to hospitals in New York, I definitely got a positive response from hospitals where I did my clinicals at and they were familiar with my program's graduates. It can definitely give you a nice edge over others.
5. Which hospitals in NY are known to hire new grads? And if they do, would they even consider a Mississippi grad?
Most hospitals in NY should hire new grads. I only looked in the city but I know that the following hire new grads: NY Presbyterian, NYU Langone (they have a 3.5 GPA cut-off), Mount Sinai, MSKCC, Maimonides, Lutheran, Bellevue, Montefiore, NY Downtown, St. Francis (Long Island), and LIJ. I know that there are plenty more but these are the hospitals where my classmates have been hired at.
6. What else can I do to boost my chances of having a successful job search in NY?
I ended up accepting a job in CA but I did get some advice from friends who have gotten jobs there. After applying, definitely follow up with the recruiter. Send an email, let them know how much you are interested in working for them. And continue to follow up, even if they don't respond to you the first time around. I had friends who just kept following up and many times, a recruiter finally responded. If you can drop off resumes, go to job fairs and open interviews to let them put a face to a name, definitely go for it. Networking, of course, is always a go. If you know anyone who works or knows someone who works at a hospital, definitely get in touch.
This is just from my personal experience. I think it's fantastic that you are looking ahead and making sure you're prepared. You have a great GPA, great extracurriculars, and it's definitely smart that you're looking into BSN and MSN programs (hospitals want to see this). Good luck in school and with your job search!