Well, I come from a military family as well, from most branches, and pretty much everyone in my family would say Air Force. Even with the Coast Guard you run the chance of being stationed on the opposite coast from your home, but you more than likely won't go overseas.
My opinion, what's the point of joining the military without going overseas. That's no fun. I have lived overseas 3 years of my life and loved it. It's best to get away and be totally on your own for a least a few years. I would at least try another branch for the lowest term you can get, which is usually 4 years, and then, if you are not happy and decided you want to go Coast Guard, have at it. Just change over as soon as you get out of one branch, don't let more than 2 months go by.