Do you know which of the 4 positions you would be applying for?
Normal GPA requirements:
Subs/SWO(N) is 3.2+
Nuclear Power School Instructor is 3.5+
Naval Reactors Engineer 3.8+
That being said, I've seen situations where someone got accepted with a 3.0 because their last 50-60 hrs were above the 3.2 mark.
The best bet is to talk to a recruiter and start the process of the appplication. There are ~10 pages to fill out and the recruiter should be able to tell you how you stack up with just that information. If it looks good, the recruiter will submit that paperwork and you will go on a VIP tour. It is a 2-3 day trip visiting a sub/aircraft carrier or visiting Power school (instructor applicants). The Navy will pay for your trip so you just need to go in with your mind open and armed with lots of questions. This will be your best chance to decide if pursuing a Naval career is what you want to do.
Once you finish the trip you will then fill out the rest of the application, apply for a security clearance, and head to MEPS to get a physical screening. Then they submit your package and you wait until you get called to interview. The whole process seems to take at least a few months and as long as a year for others. The longer time is normally due to Naval reactors requesting that you complete the next semester with a certain (3.3 or better) GPA.
I'm glad to hear you are considering serving your country. Good Luck.