I hope I fully understood what you requested. Here goes.
\tikzexternalize accepts a prefix parameter which tells pdflatex where to store the externalised graphics. So even if you use \input in main.tex to include exercises with tikzpictures, you can set prefix=<something> in main.tex to let pdflatex know that externalised graphics should be stored in that directory – specifically, you want them in the directory of the exercise. You can also separate the code from the processing by saving the externalised graphics in a sub-directory where all exercises of a chapter are stored. Here I use external as the directory.
% Macro holding the exercises directory name (in main.tex).
\newcommand{\exercisesdirectory}{aclass/achapter/exercises/}
% Macro holding the externalized sub-directory (in main.tex).
\newcommand{\externaldirectory}{aclass/achapter/exercises/external/}
\usepackage{tikz}
\usetikzlibrary{external}
% All externalized graphics go go the \externaldirectory
\tikzexternalize[prefix=\externaldirectory]
% Externalise only on-demand.
\tikzexternaldisable
There is a caveat, however: if your main file is not always named main.tex, then the external library will re-externalise graphics with a new filename (I believe the format is \jobname-figureX where X is a running counter starting from 0. This is not what you want; you want to avoid re-externalisation. Thankfully, this issue can be easily circumvented by letting pdflatex know what the externalised graphic should be named using \tikzsetnextfilename:
\tikzexternalenable
\tikzsetnextfilename{ex1fig1} % This graphic will always be named ex1fig1.
\begin{tikzpicture}
% Move along. Nothing to see here.
\end{tikzpicture}%
\tikzexternaldisable
This means that if this exercise is \input in a file main.tex and a file file.tex compiled with pdflatex -shell-escape, the external library will only create the figure if ex1fig1.pdf does not exist (or if something has changed in the tikzpicture environment etc.)
With all that in mind, your main .tex file would look like this:
main.tex
\documentclass{article}
% The path to the exercises.
\newcommand{\exercisesdirectory}{aclass/achapter/exercises/}
% The path where externalised graphics will be stored.
\newcommand{\externaldirectory}{aclass/achapter/exercises/external/}
% Will be used to store the path to the exercise to be processed.
\newcommand{\pathtoexercise}{}
\usepackage{tikz,pgfplots}
\usetikzlibrary{external}
% All auxiliary files and externalised graphics go to \externaldirectory.
\tikzexternalize[prefix=\externaldirectory]
% Only externalise on-demand.
\tikzexternaldisable
% In case you want to include externalised graphics directly.
\graphicspath{ {\externaldirectory} }
\begin{document}
% This will combine the \exercisesdirectory and "firstexercise.tex" strings,
% and store them in \pathtoexercise.
\expandafter\def\expandafter\pathtoexercise\expandafter{\exercisesdirectory firstexercise.tex}
% Then we simply input \pathtoexercise.
\input{\pathtoexercise}
\end{document}
Where firstexercise.tex is stored in aclass/achapter/exercises/.
firstexercise.tex:
This is some text from the first exercise. Below are some cool graphics.
\tikzexternalenable
\tikzsetnextfilename{ex1fig1}
\begin{tikzpicture}
\begin{axis}[%
scale only axis,
width=5cm,
height=5cm,
]
\addplot[red,samples=10] {rnd};
\end{axis}
\end{tikzpicture}%
\tikzexternaldisable
If you want to include only externalised graphics instead of the whole firstexercise.tex, all you need to do is to set the graphicspath in main.tex to the \externaldirectory, like so: \graphicspath{ {\externaldirectory} }. Thereafter, you simply use \includegraphics with the figure filename, like so:
% \includegraphics will automatically search in the graphicspath directory.
\begin{figure}
\centering
\includegraphics{ex1fig1.pdf} % This is actually in aclass/achapter/exercises/external/ex1fig1.pdf
\caption{Exercise $1$, Figure $1$}
\label{fig:ex1fig1}
\end{figure}
I hope this makes at least some sense and that it is in fact what you requested.
