The academy does most of the promotion, but a huge amount of our business is word-of-mouth. We also have a pretty strong presence in our local community press and have even had a few articles about us in the Cincinnati Enquirer. We've also received a lot of attention with the studio videos, both from the press, music forums, and even from the bands themselves and that has gotten a lot of students excited.
I've personally advertised on Craigslist, but it seems like everyone is these days and the prices are getting ridiculous. Most of my own students are referrals from current or prior students or from my business cards that I leave on community boards at bookstores, coffeeshops, etc. I have an LMA bumper sticker on my car and sometime I'll have people ask me about it in parking lots... those aren't always guitar or drum students though.