The best thing for you to do is build a list of people and reach out to them asking them to try the app. You then use that group of people to gather data about the product. Also ask the people to refer their friend.
Posting on relevant message boards, forums, twitter and the like well help with #1. For #2, you have to frame your description and talking points to the pain point that your app addresses.
#2 will help you figure out where to post and how to describe you app. What is it that you've built?
For me at least, games tend to fit one of the following two categories:
1) Fun caused by learning—whether if it's an 80's style sidescroller a racing game or a RTS, many many games are about steadily mastering skills and using them to take on progressively harder challenges.
2) Immersive stories—RPGs can offer many of the same benefits of either reading fiction or watching movies. This type is pretty rare on a mobile device, but certainly not unheard of.
In either case, a game is something I'd actively seek out, not a way of escaping "pain". I certainly don't feel a "pain" of boredom that needs to be relieved. I'm just not that morose.
I would suggest finding people on twitter who fit the typical user and mention it? I did that, posted about it on my blog and a few other things, not sure really what actually got me going, but I did get some downloads that route. If it's a good app hopefully those people will share it, I would recommend including a "share this app" link within the app
I actually wrote a great post on how I drove the first users for a product here: http://www.entrepreneur.com/article/237922
Ping me on twitter and I am happy to help you: @jsfour