From my experience, you want to really as early as possible once you have enough features to present your core idea. My partner and I spent so much time fixing every little thing, identify every little bug, because we were afraid of launching an "incomplete" alpha may turn users away. To our surprise, the early adopters are actually your best friends, they will provide you with great feedback that may change the direction of your idea completely. In our experience, our users' feedback really changed our focus on which area of the site to develop.

We wish we released earlier. So my recommendation is, once you have all your core feature to demo your idea, you should released to a group of friends/family to test it out.