How can you put items on one line and center them?

Question

Is there an easy way to make the items appear horizontally and not vertically and also be centered?

I have tried the following code but the points are squahed to the left side and there is no space in between them.

\documentclass{article}

\usepackage[inline]{enumitem}

\begin{document}

\begin{itemize*}
  \item Item 1
  \item Item 2
\end{itemize*}

\end{document}

I am thinking something like the one below where o is the "dot" made.

(space from the left side) o Item 1 (space here) o Item 2

Answer 1

You have several choices, of which I present two. The new environment would be my choice.

\documentclass{article}
\usepackage[showframe]{geometry}
\usepackage[inline]{enumitem}

\newenvironment{centeritemize*}[1][]
  {\par\centering\begin{itemize*}[itemjoin=\quad,#1]}
  {\end{itemize*}\par}

\begin{document}

\begin{itemize*}[
  itemjoin=\quad,
  before=\hspace*{\fill},
  after=\hspace*{\labelwidth}\hspace*{-\labelsep}\hspace*{\fill},
]
  \item Item 1
  \item Item 2
  \item Item3
\end{itemize*}

\begin{centeritemize*}
  \item Item 1
  \item Item 2
  \item Item3
\end{centeritemize*}

\end{document}

If you want some vertical space above and below the list, you can do

\newenvironment{centeritemize*}[1][]
  {\begin{center}\begin{itemize*}[itemjoin=\quad,#1]}
  {\end{itemize*}\end{center}}

and this shows why using a new environment is better.

Answer 2

A solution with the before and after keys from enumitem:

\documentclass{article}
\usepackage[showframe]{geometry}
\usepackage[inline]{enumitem}

\begin{document}

\begin{itemize*}[itemjoin=\quad, before=\null\hfill, after=\hskip1.5em\hfill]
  \item Item 1
  \item Item 2
\item Item3
\end{itemize*}

\end{document} 

Answer 3

Just for fun:

\documentclass{article}

\newcommand{\itemtab}{\hspace{\tabcolsep}\textbullet\hspace{\itemsep}}

\begin{document}

\begin{center}
\begin{tabular}{@{\itemtab}l@{\itemtab}l}
  Item 1 & Item 2
\end{tabular}
\end{center}

\end{document}