These are secular magazines which are available online and/or in print. All are off site.
American Atheist Magazine
A Journal of Atheist News and Thought
A British Secular Humanist Journal
The Only Freethought Newspaper in North America
A Magazine of Critical Inquiry and Social Concern
The Journal of the Society of Humanist Philosophers
A Voice for Atheists and a Standard Bearer for Atheism
The Skeptical Inquirer
The Magazine for Science and Reason
A quarterly journal promoting science and critical thinking.
A Skeptical Look at Pseudoscience and Claims of the Paranormal in the U.K.
The Skeptical Review
A Critical Examination of the Bible Inerrancy Doctrine
The Journal of Independent Thought