LGBT writing an email to start a Festival?

Honestly, writing to the mayor will do no good unless you have someone willing to lead the efforts and put in the time and energy to make these things happen. A mayor can't. They can approve and get funding, but that's about all. Are you that person who will bust their butt even though you might not get results? If you said no, then network before writing your letter to build a committee to work for this.