Just a point of clarification on nursing schools, the nursing program must be NLN or CCNE accredited. My guess is that most four year colleges with nursing programs
will be accredited by one of those agencies, but it is a requirement. Some of the other branches are specific to one agency, but the Navy will accept either.
If you know that you want to join, then for college you also have two other options to look at - attending a nursing school that has a Navy ROTC program with a nurse option. ROTC will take time away from your nursing program, but it also gives you a head start on the Navy side of things before commissioning as an officer. You can find more info along with a list of schools here Naval Reserve Officers Training Corps - Nurse Corps
Another option is to apply for the Navy Nurse Candidate program which you can do once you have your acceptance to nursing school (usually during your sophomore year of college). Here you receive a stipend while you are in school but your only task is to attend nursing school. There is no additional training, so once you graduate (& pass the NCLEX) you commission as an officer, but don't have any Navy training. You then will get some, but ROTC definitely provides you with more.
It really depends on what you are looking for and how certain your are that you want to join the Navy. Both of these options provide you a spot upon graduation but that means you have a commitment to serve, so you don't want to sign anything until you know this is what you want. You also have the option of going to nursing school and then applying to the Navy upon graduation or, more likely, after you have gained some experience.