Aligning text off-center

I would suggest using a regular tabular environment and using the column alignment character & to indicate your centering or pivot point. For example,

\documentclass{article}
\begin{document}
\ttfamily
\begin{tabular}{r@{}c@{}l}
  ABC&D&EFG \\
  GFE&D&CBA \\[10pt]
   BC&D&EFG \\
  DFE&D&CB
\end{tabular}
\end{document}

Although technically different from @egreg's answer, you could consider & to represent the "padding character" that allows you to align the pivot point. The regular tabular inter-column space has been set to zero using @{}. This ensures that the three columns have no separation between them.

Since this solution now falls within the realm of tabular, all tabular (and array) related things apply. For example, if you which to underline the pivot entry, define a new pivot column C using \newcolumntype from the array package. The following works:

\documentclass{article}
\usepackage{array}% http://ctan.org/pkg/array
\newsavebox{\colbox}
\begin{document}
\newcolumntype{C}{@{}>{\begin{lrbox}{\colbox}}c<{\end{lrbox}\underline{\usebox{\colbox}}}@{}}%
\ttfamily
\begin{tabular}{rCl}
  ABC&DEF&G \\
  G&FED&CBA \\[10pt]
   BC&DEF&G \\
  G&FED&CB
\end{tabular}
\end{document}

Perhaps you're interested in highlight (with some back colour) the pivot column. This is possible using the colortbl package (together with the xcolor package) and (say) black!15 (15% black):

\documentclass{article}
\usepackage{array}% http://ctan.org/pkg/array
\usepackage{colortbl}% http://ctan.org/pkg/colortbl
\usepackage{xcolor}% http://ctan.org/pkg/xcolor
\begin{document}
\renewcommand{\tabcolsep}{0pt}
\newcolumntype{C}{@{}>{\cellcolor{black!15}}c@{}}%
\ttfamily
\begin{tabular}{rCl}
  ABC&DEF&G \\
  G&FED&CBA \\[10pt]
   BC&DEF&G \\
  G&FED&CB
\end{tabular}
\end{document}

You can define a "padding character"; in the following code I've used ? (it must be a character you don't otherwise use inside the environment):

\documentclass{article}
\newenvironment{ttcenter}[1][?]
  {\begin{center}\catcode`#1=\active
   \scantokens{\def#1{\leavevmode\phantom{A}}}\ttfamily}
  {\end{center}}

\begin{document}
\begin{ttcenter}
ABCDEFG\\
GFEDCBA\\[10pt]
?BCDEFG\\[10pt]
GFEDCB?
\end{ttcenter}
\end{document}

Also the input will be "visually aligned". If you need another character, specify it as the optional argument:

\begin{ttcenter}[-]
ABCDEFG\\
GFEDCBA\\[10pt]
-BCDEFG\\[10pt]
GFEDCB-
\end{ttcenter}

A simpler way, if the "padding" goes only on one side of the letters is

\newenvironment{ttcenter2}
  {\begin{center}\ttfamily\begin{tabular}{@{}c@{}}}
  {\end{tabular}\end{center}}


\begin{ttcenter2}
        ABCDEFG\\
        GFEDCBA\\[10pt]
\hfill   BCDEFG\\[10pt]
        GFEDCB\hfill
\end{ttcenter2}

The "padding character" version is needed if, for instance, there are holes.

You could simply use \phantom{} macro to insert space equivalent to the characters that were removed:

\documentclass{article}
\begin{document}
\begin{center}
    \texttt{\phantom{A}BCDEFG}\\
    \texttt{GFEDCB\phantom{A}}
\end{center}
\end{document}

While this will solve the given code example, the solutions provided by @egreg and @Werner provide additional flexibility and may be more appropriate depending on exactly what you need.