First of all, for everyone who thinks that this would look "desperate" to medical schools - this isn't dating. It's applying to professional school. I doubt they'd see the OP as desperate - they are much more likely to think "wow, this kid obviously really wants to come here for an interview". Now, if an interview is not forthcoming, is a letter stating that you're always in the area going to help? Probably not. Additionally, medical schools are aware of who on their "potential interview" list is in the area, and will call them in at the last minute if needed, so I don't really think there's any need to point this out to them, unless you have moved since your initial application. You'd be better off writing a letter of interest explaining why you like the school, and stating that you live in the area and really like it there (or have family there, or whatever your connection is) and therefore you'd really like to stay for medical school, which is only #210 why you LOVE their school.
Also, to whoever said that they're more likely to invite someone to interview if they're only in the area for a short time, versus someone who's always in the area - also not true. They're going to invite whoever is next on their list of people they want to interview.