Typesetting on block matrix is ugly

Another option would be to use a two-column array:

\documentclass{article}

\begin{document}

\[
\left(
\begin{array}{c|c}
  1 & c_2 \cdots c_n \\ \hline
  0 & \raisebox{-15pt}{{\huge\mbox{{$A$}}}} \\[-4ex]
  \vdots & \\[-0.5ex]
  0 &
\end{array}
\right)
\]

\end{document}

Although there are some personal preferences built into this question (and therefore some subjectivity), I have some suggestions.

You can play around with the vertical alignment using the graphicx package command \raisebox{<height>}{<stuff>}:

\usepackage{multirow}% http://ctan.org/pkg/multirow
\usepackage{graphicx}% http://ctan.org/pkg/graphicx
...
\[
  \left(\begin{array}{c|ccc}
    1 & c_2 & \cdots & c_n \\ \hline
    0  & \multicolumn{3}{c}{\multirow{3}{*}{\raisebox{-7mm}{\scalebox{2}{$[A]$}}}} \\
    \raisebox{2pt}{\vdots} & & &\\
    0 & & & 
  \end{array}\right)
\]

I've also added some brackets around the inner matrix A to accentuate the fact that it could be considered a matrix. The size of the inner/sub-matrix has also been set using \scalebox{<factor>}{<stuff>} from the graphicx package, since \Huge is a textmode font command. Using colour for certain parts of the matrix may also highlight the scope of the matrix. In the example below, cells within the array were coloured using 10% black (via black!10):

\usepackage{xcolor}% http://ctan.org/pkg/xcolor
\usepackage{colortbl}% http://ctan.org/pkg/colortbl
\usepackage{graphicx}% http://ctan.org/pkg/graphicx
...
\[
  \left(\begin{array}{c|ccc}
    1 & c_2 & \cdots & c_n \\ \hline
    0  & \multicolumn{3}{c}{\cellcolor{black!10}} \\
    \raisebox{2pt}{\vdots} & \multicolumn{3}{c}{\cellcolor{black!10}\scalebox{2}{$[A]$}} \\
    0 & \multicolumn{3}{c}{\cellcolor{black!10}}
  \end{array}\right)
\]

At lower resolution the coloured matrix may should some problems. However, this should only be visible in your viewer and not the actual print.

Alignment of the brackets around the matrix can also be adjusted, but I'm not sure whether this is part of the "can't quite put my finger on [it]" part.