Your gap year might best be used as a scouting trip. Sometimes the place that most captures your imagination turns out to be exactly where you don't want to live. A place that you never had considered may fit so well you never want to leave. You won't know until you visit.
HOW TO PAY YOUR WAY If it were me today, I would look for work that offered some degree of physical control over my day and the ability to listen to high-level conversations undetected. Janitorial for interesting companies, non-profits and museums would be my ticket. When it was me, twenty years ago, I did quite a bit of restaurant work supplemented with targeted freelance and internships. Restaurants usually provide a free meal during your shift. (Get friendly with a cook and you can go home with sandwiches to cover your days off as well.) Freelance keeps you from being ground down by the physical exhaustion and constant ego blows of a "low skill" position- and if it makes you some money, well, Yahtzee for you.
LIVING TIPS Shared room situations and furnished sublets will keep you lease-free but be sure you have a way to lock up your stuff while you are at work. Pay your sub-let rent by check or money order to maintain a paper trail. Often the landlord will not know you are there and this covers your butt. Also, even friendly, straight-A student, drug users will "borrow" from you eventually.
HOW TO STAY SANE If not freelance, any structured learning will help buoy you psychologically but be sure to connect with someone who will hold you accountable for turning in something every week. Another option is http://www.straighterline.com/ or some other MOOC program. The added bonus is you can tell your grandparents you are in a distance, college program. Even if the university you eventually attend does not accept your MOOC credits, you can often "challenge" a course and, by proving you have mastered the material, be passed out of it.
TOTALLY DO-ABLE Resourceful people capable of teaching themselves can survive. A resourceful person who knows a portable skill like coding, is single, child free, 17-19 year old, willing to ask for help, and has a middle class background is well equipped for a gap year. You won't starve. Travel lightly and take photos.