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I can find a lot of resources that show the inverse, (expressing cylindrical in terms of of Cartesian) but I just can't find what I want.

My wild guess is : $\hat{i} = -\sin{\theta} \;\hat{\theta} \\ \hat{j}=\cos{\theta}\;\hat{\theta} \\ \hat{z}=\hat{z}$

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    This was the first link when I googled "cylindrical coordinates to cartesian": http://tutorial.math.lamar.edu/Classes/CalcIII/CylindricalCoords.aspx – 2017-02-27
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    I love Paul's notes, what I want is certainly not on there. – 2017-02-27
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    If iIm not mistaking, you are asking for an expression of Cartesian coordinates $(x, y, z)$ in terms of cylindrical coordinates $(r, \theta, z)$. This is a widely available result: \begin{eqnarray} x &=& r \cos \theta \\ y &=& r \sin \theta\\z&=&z\end{eqnarray} – 2017-02-27
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    Ah, I see the confusion. I wanted the cartesian unit vectors in terms of the cylindrical unit vectors, which is what zahbaz supplied. – 2017-02-27

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Cartesian $(x,y,z)$ to cylindrical $(\rho,\phi,z)$,

\begin{align} \hat{x} &= \cos\phi \hat{\rho} - \sin\phi \hat\phi \\ \hat{y} &= \sin\phi \hat{\rho} + \cos\phi \hat\phi \\ \hat{z} &= \hat z \end{align}

From Griffith's Introduction to Electyrodynamics, inside back cover.