I accept Jung's position that even without a deity or supernatural governor, everyone ultimately holds a faith.
If you are trading in your old faith for a new one, it is always better not to define yourself by contrast. Dawkins philosophy of opposing religious thinking completely is ultimately an impossible task. Even structures like science and government involve things that are ultimately faith-based reasoning. (Why do we trust in the existence of universal principles? To what extent do we believe that logic matters? Upon what do we wish to found our notions of value? -- These are issues of choosing a faith.)
So the answer here depends upon what part of your old faith is not working for you, and by what contradictions or weaknesses you are motivated to leave religion. Without more data, moving away from any one thing does not give you a destination. And any complete worldview requires a destination, not just an enemy.
But, choosing rather randomly (between three folks upon whom I rely for a lot of context that I consider faith-based) to my mind, one of the saner explicitly atheist philosophers, who addresses his divergence from traditional beliefs in a way that is not just an escape, but a productive refinement, is Daniel Dennett. He is one of the most prominent spokesmen of the 'Brights Movement', after Dawkins, and he is also genuinely a philosopher, and not just a critic -- so he is less dismissive, attacking and rash than Dawkins.
One of his basic philosophical motivations is to replace the remnants of the 'Cartesian Theater': the idea that the mind and the body are completely separate in any way. This seems like a strange foundation on which to build any sort of global understanding of the world, but it results in a thoroughgoing reorganization of a lot of basic philosophical notions that we all fail to question, and that fit together nicely to explain ourselves without being too dominating.
It takes us closer to nature by emphasizing the continuity of evolution and diminishing the 'miracle' of the 'origin' of the mind. Humanistic traditions often still worship the mind as miraculous after they have decided there are no miracles, which is a counterproductive hypocrisy. Dropping it makes us think about why we adopt the moral standards that we do, and what we might all learn by being less special.
The notion of the parallel nature of all biological processes challenges us to look at our minds in a more realistic way that is not tied directly to our stream of consciousness, more like the way we look at our bodies. Meditation and prayer, setting aside the stream of consciousness and our individuality is then not some kind of sacrifice, mystical goal, escape from reality or feat of casting ourselves upon the mercy of some higher being. It is a natural part of self-exploration that constitutes another, more deeply aesthetic, dimension of natural thought that we neglect when we dwell in the conscious mind.
Theories of meaning that do not descend from human language but upon deeper considerations of how the parallel and serial processes of our minds can construct one another, point out how much life is story-driven and how we impose sequential processes because of our attachment to social cues. This doesn't dissolve our attachment to mythology, but leans back toward Jung, and puts it in context as a necessary part of the way humans think.