Displaying a later value of a counter
You need to use the \label-\ref system.
First of all you don't need to reset manually your counter, it suffices to bind it to chapter:
\newcounter{mycounter}[chapter]
Next I'd use the refcount package and issue a \label just before doing \chapter together with \refstepcounter{mycounter} (this will give an "off by one" which is easily corrected):
\usepackage{refcount}
\newcounter{mycounter}[chapter]
\newcommand{\newchapter}[1]{%
\refstepcounter{mycounter}\label{mycounterref@\thechapter}%
\chapter{#1}
(The value of \texttt{mycounter} at the end of this chapter will be
\number\numexpr\getrefnumber{mycounterref@\number\value{chapter}}-1\relax)\par}
\AtEndDocument{\refstepcounter{mycounter}\label{mycounterref@\thechapter}}
Of course, the first compilation won't give the actual number as usual for the \label-\ref system.
The solution by egreg is useful because it calls \refstepcounter, which might be needed for things other than printing a counter's state/number. But here is a solution that needs no refcount package and no \refstepcounter, thereby being cheaper. It requires a command, but not a label, per each chapter. I have used Bruno Le Floch's example text from here.
\documentclass{book}
\makeatletter
\newcounter{mycounter}
\newcommand{\newchapter}[1]{%
\chapter{#1}%
\ifnum\thechapter<\tw@\else
\immediate\write\@auxout{%
\global\noexpand\@namedef
{mycounter\the\numexpr\thechapter-1}{\number\c@mycounter}%
}%
\fi
\setcounter{mycounter}{0}%
\@ifundefined{mycounter\thechapter}{}{%
\textcolor{red}{The value of \texttt{mycounter} at
the end of this chapter is \@nameuse{mycounter\thechapter}.}\medskip
}%
}
\AtEndDocument{%
\immediate\write\@auxout{%
\global\noexpand\@namedef{mycounter\thechapter}{\number\c@mycounter}%
}%
}
% All the following is just an example text.
\newlength{\sos@top}
\newlength{\sos@right}
\newcounter{sos@pages}
\newif\ifSOS
\renewcommand{\thepage}{\the\numexpr\value{page}-\value{sos@pages}\relax}
\newcommand{\addfig}[1]{\g@addto@macro\sos@figures{\vbox{\centering#1}\vfill}}
\newcommand{\sos@reset@figures}{\gdef\sos@figures{\sos@reset@figures\vfill}}
\sos@reset@figures
\newcommand{\sos@shipout@figures}{%
\begingroup
\stepcounter{page}%
\stepcounter{sos@pages}%
\let\protect\relax
\setbox\z@\vbox to\vsize{\sos@figures}%
\let\protect\string
\AtBeginShipoutOriginalShipout\vbox
{\vbox to\sos@top{}\moveright\sos@right\box\z@}%
\endgroup
}
\AtBeginShipout{%
\ifSOS
\ifodd\c@page
\begingroup
\let\protect\string
\AtBeginShipoutOriginalShipout\box\AtBeginShipoutBox
\AtBeginShipoutDiscard
\sos@shipout@figures
\endgroup
\fi
\fi
}
\newcommand{\SOSshipout}{\clearpage\sos@shipout@figures}
\renewcommand{\SOStrue}{\clearpage\global\let\ifSOS\iftrue}
\renewcommand{\SOSfalse}{\clearpage\global\let\ifSOS\iffalse}
\setlength{\sos@top}{2cm}
\setlength{\sos@right}{2cm}
\newcommand*\lipsumnopar[2][1]{{\def\lips@par{ }\lipsum[#1-#2]}}
\makeatother
\usepackage{booktabs,caption}
\usepackage{atbegshi,xcolor}
\usepackage{lipsum}
\usepackage{hyperref}
\begin{document}
\title{Hello world}
\author{Bruno Le Floch}
\maketitle
\tableofcontents
\listoffigures
\listoftables
\part{Abc}
\SOStrue
\newchapter{Hello}
\noindent{\bf\texttt{mycounter} is called 3 times in this chapter.}\medskip
\addtocounter{mycounter}{1}
\addfig{\begin{tabular}{p{5cm}p{5cm}}
\toprule
Abc def & ghijk lmno pq \\
\midrule
\lipsum[1] & \lipsum[2] \\
\bottomrule
\end{tabular}
\captionof{table}{\label{tab:atable}A table}
}
\addfig{%
\rule{8cm}{3cm}%
\captionof{figure}{A figure}
}
\lipsumnopar{10}
\addfig{\rule{1cm}{3cm}\captionof{figure}{Another figure}}
\addfig{\rule{8cm}{3cm}\captionof{figure}{A figure}}
\addfig{\rule{1cm}{3cm}\captionof{figure}{Another figure}}
\addtocounter{mycounter}{1}
\addtocounter{mycounter}{1}
\newchapter{Bye}
\noindent{\bf\texttt{mycounter} is called 2 times in this chapter.}\medskip
\addtocounter{mycounter}{1}
\addfig{\rule{8cm}{3cm}\captionof{figure}{That should be figure 5.}}
\addfig{\rule{1cm}{3cm}\captionof{figure}{Perhaps the sixth}}
\lipsumnopar{10}
\addfig{\rule{8cm}{3cm}\captionof{figure}{Yet another one}}
\addfig{\rule{1cm}{3cm}\captionof{figure}{One last figure for now.}}
\SOSfalse
\addtocounter{mycounter}{1}
\newchapter{Back to normal}
\noindent{\bf\texttt{mycounter} is called 3 times in this chapter.}\medskip
\addtocounter{mycounter}{1}
\addtocounter{mycounter}{1}
\addfig{\rule{8cm}{3cm}\captionof{figure}{That figure won't be lost.}}
\lipsumnopar[11]{15}
\addfig{\rule{4cm}{5cm}\captionof{figure}{Nor will that one.}}
\lipsumnopar[16]{20}
\lipsumnopar[21]{30}
See Table~\ref{tab:atable}.
\SOSshipout
\SOStrue
\addtocounter{mycounter}{1}
\newchapter{Figures, again}
\noindent{\bf\texttt{mycounter} is called 1 time in this chapter.}\medskip
\addtocounter{mycounter}{1}
\addfig{\rule{5cm}{2cm}\captionof{table}{Let's pretend it's a table}}
\lipsumnopar[21]{25}
\addfig{\rule{5cm}{2cm}\captionof{table}{Let's pretend it's a table}}
\lipsumnopar[26]{30}
\addfig{\rule{4cm}{1cm}\captionof{table}{Last table}}
\end{document}
Edit:
Here is my attempt to generalize the solution. More testing is required.
\makeatletter
\newcommand\ifstrsame[2]{%
\@nameuse{@\ifnum\pdfstrcmp{\detokenize{#1}}%
{\detokenize{#2}}=0first\else second\fi oftwo}%
}
\def\appchap#1{\ifstrsame{chapter}{#1}{}{\thechapter}}
\def\headingnr#1{%
\ifstrsame{section}{#1}{%
\expandafter\getheadingnr\romannumeral-`\q\@nameuse{the#1}..\relax
}{%
\number\@nameuse{the#1}%
}%
}
\def\getheadingnr#1.#2.#3\relax{#2}
\def\newchapter@hook{}
\def\DeclareCallsCounter#1#2{%
\newcounter{#2}%
\expandafter\newcommand\csname new#1\endcsname[1]{%
\ifstrsame{section}{#1}{%
\gdef\newchapter@hook{%
\immediate\write\@auxout{%
\global\noexpand\@namedef
{\appchap{#1}#2@\headingnr{#1}}{\number\@nameuse{c@#2}}%
}%
}%
}{%
\newchapter@hook
}%
\@nameuse{#1}{##1}%
\ifnum\headingnr{#1}<\tw@\else
\immediate\write\@auxout{%
\global\noexpand\@namedef
{\appchap{#1}#2@\the\numexpr\headingnr{#1}-1}{\number\@nameuse{c@#2}}%
}%
\fi
\setcounter{#2}{0}%
\@ifundefined{\appchap{#1}#2@\headingnr{#1}}{}{%
\textcolor{red}{The value of \texttt{#2} at
the end of this #1 is \@nameuse{\appchap{#1}#2@\headingnr{#1}}.}\medskip
}%
}%
\AtEndDocument{%
\immediate\write\@auxout{%
\global\noexpand\@namedef
{\appchap{#1}#2@\headingnr{#1}}{\number\@nameuse{c@#2}}%
}%
}%
}
\DeclareCallsCounter{chapter}{chapcounter}
\DeclareCallsCounter{section}{seccounter}
\makeatother