I have worked with Facebook to get it rolling, using this as a test for the next step - iAds. I am looking for advice on other ways to promote and market the app.
Great question! Facebook is a good start since you can target your audience and measure your results.
Since you recently launched your app, I'd recommend a mini-launch campaign around it. You can put together a variety of marketing tactics that all work together to spread the word about your new app.
For example, reaching out to app review websites, sending a press release, working on your App Store Optimization, and more.
Would be glad to talk any time and explain more.