In Hawaii the lot is a dirt lot, with no cover. I came back after 6 months and trashed the car cover I had put on it, and it took the better part of an hour to cut out all the weeds and small trees that were growing up through the wheels.
Next deployment, I just overinflated the tires, changed oil, and put it on a battery tender in my garage. Much better experience. Started right up, no complaints.
Were I single for the second go, I'm not sure the loss of BAH would have been worth it to keep the car garaged, but I was married, so I was stuck paying for the house anyway.
North Island, OTOH, has covered carports in a paved lot, walking distance from the pier.
As far as going car-less, I've never seen a base anywhere with "good" accommodations for the car less. North Island is not good, Norfolk is impossible. Kaneohe, for example, is full of very junior sailors and marines who can't/don't buy cars and you see them shuffling around everywhere in the hot sun like zombie extras on a Walking Dead set.
That said, after a deployment, you will find yourself with enough cash on hand to seriously consider taking on an IV drug addiction. Buying a new car post-deployment is a time-honored Navy tradition. Just, make sure and do it with cash, not the $1000 down, 54.9% APR financing most of my TEDs seem to want to use every time . . .