Where to publish (recreational) mathematics without a PhD? I have been out of undergrad for some time now but was interested in publishing a few things I have been working on. Are there any good "beginner" journals where someone without a mathematics PhD might have a chance at publishing something? 

It might be important to note that most of the material would likely just be more on the recreational side of things.

Thanks in advance.
Of the journals of the Mathematical Association of America, you can choose between The American Mathematical Monthly, the Mathematical Magazine, and The College Mathematics Journal. The three have (perhaps subtly) different scopes1, and short of you telling us exactly what your results are about we cannot tell you which journal is the best choice. (On the other hand, you can easily write to the editors of one of those three journals to see where your manuscript would best fit.) 

As Dirk mentioned, The Mathematical Intelligencer is also an obvious choice (again, caveats about not knowing whether your paper fit in their scope). 

If you aim the material at the mathematical maturity level between secondary (high school) education and first years of a college education, two good publications are Pi in the Sky which is published by the Pacific Institute of Mathematical Sciences, and Parabola which is backed by the University of New South Wales in Australia. 

Another general mathematics magazine you can try is Plus Magazine based at Cambridge; the editors specifically asks you to contact them in advance if you want to write for the publication. 



1 A very rough guide is that in terms of "mathematical maturity", the "age" of the readers are such that CMJ &lt; MM &lt; AMM.