Centered box, text inside it flushed right?

Use the varwidth package:

\documentclass{article}
\usepackage{showframe}% http://ctan.org/pkg/showframe
\usepackage{varwidth}% http://ctan.org/pkg/varwidth
\begin{document}
Here is some text. Here is some text. Here is some text.
Here is some text. Here is some text. Here is some text.
Here is some text. Here is some text. Here is some text.

\begin{center}
  ​\begin{varwidth}{\textwidth}
    Here is some title that is somewhat long. \par
    And some notes. \\
    And some more notes.
  \end{varwidth}
\end{center}

Here is some text. Here is some text. Here is some text.
Here is some text. Here is some text. Here is some text.
Here is some text. Here is some text. Here is some text.
\end{document}

A width of \textwidth for the varwidth environment makes sure that the text will fit within the text block, but also shrink to the natural width of the box (in case it's not as wide).

For keeping the title centred (if the notes extend beyond the width of the title), you can use

\begin{center}
  ​\begin{varwidth}{\textwidth}
    \centerline{Here is some title that is somewhat long.} \par
    And some notes. \\
    And some more notes. And some more notes. And some more notes.
  \end{varwidth}
\end{center}

However, you are required to use \par to the title here then. There are other ways to do this as well.

The showframe package merely highlights the "centred-ness".

You can use the minipage or the varwidth environment for the text. Then put the whole thing in a center environment.

\documentclass{article}

\usepackage{varwidth}
\usepackage{lipsum}
\begin{document}

\lipsum[1]% dummy text

\begin{center}
    \begin{varwidth}{5cm}
        \textbf{Some title}\\
        Node 1\\
        Node 2 
    \end{varwidth}
\end{center}

\lipsum[2]% dummy text

\end{document}

Of course you can use adjustbox to simplify the code a little. However the env key is unfortunately broken in the current version. I will upload a fix soon to CTAN.

\documentclass{article}

\usepackage{adjustbox}
\usepackage{lipsum}
\begin{document}

\lipsum[1]% dummy text

% Add `varwidth` and `center` environment (but broken in current version :-( )
\noindent\adjustbox{varwidth=5cm,env=center}{% 
        \textbf{Some title}\\
        Node 1\\
        Node 2
}

\lipsum[2]% dummy text

\noindent\adjustbox{varwidth=5cm,center,margin=0pt \bigskipamount}{% (`margin` adds a vertical skip above and belo)
        \textbf{Some title}\\
        Node 1\\
        Node 2
}

\lipsum[3]% dummy text


\end{document}

If the lines don't need wrapping, then there is a simple method without extra packages:

\begin{center}
\begin{tabular}{@{}l@{}}
Some centered text\\
note1\\
note2
\end{tabular}
\end{center}