I am finishing my BSN and have talked with a Navy recruiter. According to him you have to have at least 90 days experience with your BSN before you are even considered. And that is if you have experience as a nurse with your ASN. I have 7yrs and was told "great, but is that with your BSN?" When I said no, then he said "Well then it doesn't matter". He was just a peach to talk with. If you are a straight-up new grad, I am not sure what type of time frame you are looking at, but the impression I got was it's not too pretty because of budget tightening.
Now, as far as deploying. Not to sound like a Debbie-Downer, but if you're not wanting to go far from home, I hope you are already near a naval base with your specialty. Because once you are in the military, it's no longer about what YOU want, it's about what the Navy wants. I am applying to the Air Force, and I know I will be deployed at some time because I am an ER nurse with a Trauma specialty (I am a Trauma Nurse Specialist in Missouri/Illinois). It's going to happen. I have already made peace with it and understand I won't see my 2yr old son for a while when I do, nor will I see my husband or mom who is my dependant. But, it's not about how much it will suck for me, its what the AF will need and what the men and women overseas will need. Unless I get pregnant around the time of my deployment, I am going in understanding that the Air Force comes first, me and my family needs are second. Otherwise, if staying near home is what you want and are not wanting to deploy, you may want to consider the Reserves instead of Active duty. Because I can almost gaurantee you will deploy if you go Active. With the current draw down of troops, if you go reserves, you may not (though that is NEVER a guarantee either).
Going into the military is a massive decision, but I know this is the route I want to go. I wish you luck! Have you considered the possibility of trying to maybe do a job-shadow at a naval facility to see if you even like it? It may save you a lot of time and make the decision much easier for you.