How much free time do you have while serving in the Navy?

It all depends on your particular Rate and Rank. There is always something to do if you're assigned to a ship or submarine, whether you're junior, senior, enlisted or officer. However, in port, if you don't have duty (watch sections where you're required to stay onboard all night after working hours, usually every 4 days for most afloat units) then it's pretty much like a typical civilian workday - 7-4:30, if you've got your work done. Some days are more intense, others less so. It varies. If you're a division leader like I was, days and work are much longer and free time much less. But responsibility is what it is, and if you've got it, you've no choice but to do your best to make sure things are done properly.

For shore commands, they have it a bit better, as the amount of personnel lets them get away with much longer duty rotations. My wife only had duty every 30 days when she was stationed at Mine Warfare Command.

Underway, your time is determined by the mission, your particular job, all-important and endless training, etc. In general, once you've got your qualifications and major training out of the way, off duty you can relax a bit. But if you're not qualified, you'd best not be caught "relaxing". Until you're qualified to do your job on board a ship, you're a liability, and treated by the crew as such. "Useless Oxygen Breather" is what we used to term it in the Submarine Force for guys not qualified in anything.

I will say this - when you're home, all you want to do is go back to sea; when you're at sea, all you want to do is go home. But I wouldn't trade the experience or what it did for my life for anything at all. Being at sea on any Navy vessel, be it Submarine or Ship, is a unique experience, though I've always preferred submarines to ships.