I wouldn't let my 16 or 17 year old go overseas alone; however, I'm constantly surprised at how different other people's opinions are on this subject!
I was in charge of a group of high school seniors who planned a trip to Disney's Grad Nights a few years ago, and I was amazed at their naivity. Example: they tried to talk me into a 2 AM room check. Yeah, right. I'm going to let 17 and 18 year old girls from a small town stay out until 2 AM in Orlando, a town where they know no one. These were good kids -- no, they were great kids. They just didn't yet have a realistic picture of what is safe and not safe.
Do check into the hotel's age requirements. I think most of them will require at least one person who is 18 -- possibly older.
I'd reconsider the staying off-site idea. Yes, it's cheaper, but on-site is probably safer -- especially for two teens alone. The transportation will also be much easier, so you'll have one less thing to worry about.
If you do stay off-site, I assume you won't be renting a car. I know they don't rent cars to people under 21 (and some places are 25). That means you'll be relying on the hotel shuttles, most likely. Be sure to find out when these run. Disney's transportation runs constantly all day long; many off-site hotels run theirs much less frequently. Also, you should have a back up plan (i.e. taxi money) in case you are left behind by off-site transportation.
Read these boards and www.wdwig.com to figure up your food costs, etc. If you're not used to managing your own money, consider making up envelopes for each day's food spending, souveniers, the hotel, transportation back to the airport, etc. so that you won't suddenly realize that you're out of money before you're out of trip.
