Hi Marcie,
I have to insert a disclaimer here about my Navy experience - I got out in 1994 and hubby got out in 1996. Any information I have is several years old. The other thing is that we were both enlisted, as a navy nurse you will be an officer and the rules are a bit different for o-gangers than the enlisted.
You asked about housing and housing allowance. We were stationed in Pearl Harbor, one of the most expensive places to live in the country. We chose to live on base because of a quirk in the rules that applies to couples that are both in the Navy - I could go into details in a PM if you want to know, but I would imagine rules have changed since then anyway. The Navy does give a Basic Housing Allowance (BHA) and then in some more expensive parts of the world, a variable housing allowance (VHA) to help make up the difference in high rent areas. For most people it is enough to get a decent apartment or small home. We know folks that chose to buy a home in Hawaii many years ago that made money hand over fist when it came time to sell - but that's not for everyone - and they did it with their housing allowance. BTW, housing allowance is tax free, it's an allowance, not income

.
Base housing all depends on the base. If you are a single officer, you will have two choice 1) the BOQ (Basic Officer Quarters) which is proably more like a very small apt or hotel room with a refer and microwave or 2) take your BHA etc... and rent a place on the town. If you are married then you may have the option of living in base housing. We had everything from beach front cottages, nice apartments or what we fondly referred to as 'flinstone' housing (flat roofs, small, etc). The nice thing about housing is that we had a washer, drier, dishwasher and access to free use of all sorts of lawn equipment to borrow for free. If anything broke, we just called housing and they came out and fixed it. Bad part was it was like living in a community with 'covenants' on sterioids. Lawn couldn't get long, could only have so many pets, could only paint certain colors, etc... Not very private, but then again, our neighbors really were our family.
I would get very specific information from the nurse recruiter and then GET EVERYTHING IN WRITING!!!!!! Remember everything that you get to do in the Navy is based on the needs of the Navy, not necessarily what you want. It's wonderful when what you want meets those needs though.
As far as becoming a SANE nurse: Sexual Assault happens everywhere. I would hate to speak for what the military is like today, but I know you watch the news like everyone else and where there is smoke, there is at least a little spark if not a fire. I think having a SANE nurse available at every base clinic should be mandatory, no matter how big or small the base is.
The sexual politics, harrassment and abuse are a reality. Is the military getting better about dealing with it - yes, is the problem solved - no. Is it just a military problem - no, it is a problem everywhere in the world. I will just add that when I go for my annual physical with the VA, one of the standard questions on the admission form is something to the effect of was I ever raped or the victim of unwanted sexual advances. I don't know many female vets that did not have to deal with some sort of sexual misconduct whether it was sexual harrassment to flat out rape - we all delt with it at some level.
Please don't let what I have told you discourage you from the Navy, I would do it all again if I had the chance. You may want to consider looking into the Air Force programs as well.
Good luck, Heather