Pros
The Navy can be wonderful. They offer steady pay, housing, and sometimes the opportunity for travel and seeing other parts of the world. You also have access to the GI bill for further education, VA loans for purchasing a home, and free healthcare.
Cons
You work on salary, which means that you get paid the same whether you work 30, 40, or 60 hours per week. In my experience, you almost always work more hours, not less. Because of this, there is often a poor work/life balance. In addition to your job, you will be required to have additional task or responsibilities, known in the military as "collaterals". For Officer advancement, it is these collaterals that often determine whether you will advance to the next rank. The system is broken. Advancement should be based on how well a person performed their job, not how many or what kind of extra tasks or duties they take on. In addition, you have little to no say in what kind of job you will do (even as a nurse, the type of nursing job will have is largely outside of your control). If you want to choose what job you will be doing, do not join the Navy. In addition, as a supervisor, it is very difficult to 'fire' a person, even if they are unqualified and unfit to do their job. Often, people with performance problems are passed from department to department, and even eventually promoted.