How to do something like "inner sep west"? -- specify inner sep on just only one side

Using \hspace* you can manually control the padding:

\documentclass{article}
\usepackage{tikz}

\begin{document}

\begin{tikzpicture}
\node [inner xsep=10pt, draw=blue, very thick, rectangle] (a) at (0,0) {\hspace*{20pt}Some Text in here};
\node [inner xsep=30pt, draw=blue, very thick, rectangle] (d) at (0,-1) {Some Text in here\hspace*{-20pt}};
\node [inner xsep=10pt, draw=blue, very thick, rectangle] (b) at (0,-2) {Some Text in here\hspace*{20pt}};
\node [inner xsep=30pt, draw=blue, very thick, rectangle] (c) at (0,-3) {\hspace*{-20pt}Some Text in here};
\end{tikzpicture}

\end{document}