Putting together a home gym is one of the best decisions I ever made. I sold my motorcycle to pay for most of the equipment. Essential equipment for me was: power rack, good barbell, mix of iron and bumper plates, horse stall mats (cheapest rubber flooring I could find), and a home made lifting platform (plywood and another stall mat).
I turned half of my detached uninsulated garage into my gym. I live in Michigan so the winters (particularly this one) can get cold and the summers are at times kind of humid, but I'll take my own gym at 10 degrees over a climate controlled globo gym any day.
Biggest advantages that immediately come to mind: chalk, nice equipment i never have to wait for, I can grunt/yell as loud as I want without worrying about anyone's reaction, no contract or monthly fee, free weights don't wear out so not much worry about replacing equipment, did I mention chalk?
Disadvantages: nothing worth noting since being out in extreme temperatures just makes you more adaptable ;)
I have never had a problem keeping the intensity up without other people around. I do have a friend who lifts with me most of the time, but there is no backing off if he isn't around.
Is your GF receptive to learning how to lift weights? If so, maybe you can get her to see it as an advantage to have a home gym.