This is possible when using the zref package. Loading the user module (or directly via the zref-user package) you have access to a number of properties associated with a \zlabel (similar to LaTeX's \label).

\documentclass[twoside]{article}
\usepackage[margin=5mm,paperheight=2in,paperwidth=4in,bottom=15mm]{geometry}% http://ctan.org/pkg/geometry
\usepackage[user]{zref}% http://ctan.org/pkg/zref
\newcounter{refcnt}% Counter used with every reference
\makeatletter
\newcommand{\myref}[1]{%
\stepcounter{refcnt}\zlabel{#1@\therefcnt}%
\texttt{#1} is on page~\zref[page]{#1}.
This is page~\zref[page]{#1@\therefcnt}. \par
\texttt{#1} is on a~\ifodd\zref@extract{#1}{page}recto\else verso\fi~page.
This is a~\ifodd\zref@extract{#1@\therefcnt}{page}recto\else verso\fi~page. \par
\texttt{#1} is
\ifnum\zref@extract{#1@\therefcnt}{page}=\zref@extract{#1}{page} % same page
on this page.
\else
\ifnum\numexpr\zref@extract{#1@\therefcnt}{page}-\zref@extract{#1}{page}\relax=1 % previous page
\ifodd\zref@extract{#1@\therefcnt}{page}
on the left-hand page.
\else
on the previous page.
\fi
\else
\ifnum\numexpr\zref@extract{#1}{page}-\zref@extract{#1@\therefcnt}{page}\relax=1 % next page
\ifodd\zref@extract{#1@\therefcnt}{page}
on the next page.
\else
on the right-hand page.
\fi
\else
\ifnum\zref@extract{#1}{page}>\zref@extract{#1@\therefcnt}{page} %
\strip@pt\dimexpr\zref@extract{#1}{page}pt-\zref@extract{#1@\therefcnt}{page}pt\relax~pages ahead.
\else
\strip@pt\dimexpr\zref@extract{#1@\therefcnt}{page}pt-\zref@extract{#1}{page}pt\relax~pages before.
\fi
\fi
\fi
\fi
}
\makeatother
\begin{document}
This is~\texttt{foo}.\zlabel{foo} \par \medskip
\myref{foo}
\newpage
\myref{foo} \par \medskip
\myref{bar}
\newpage
\myref{foo} \par
This is~\texttt{bar}.\zlabel{bar}
\newpage
\myref{bar}
\end{document}
For each label <lab> that is referenced via \myref{<lab>}, a new \zlabel <lab>@<refcnt> is set where <refcnt> is an ordinary running counter. This allows for extracting properties associated with <lab>@<refcnt> to perform calculations with.
\zref@extract{<ref>}{<prop>} provides an expandable version of the property <prop> of label <ref>, allowing for calculations. In the above example, recto and verso pages are decided based on whether page is odd/even.
\myref could be expanded to include line referencing using the savepos module, which would allow for referencing "...above, on this page." or "...below, on this page." This would be achieved by using the expandable \zposy{<lab>} to extract the y-coordinate of the label <lab> on the page and comparing it to some other label.
Note that you have to compile at least twice for the references to "settle," despite possible errors that LaTeX complains about during the first run.