Don't nest TikZ pictures (unless you really have to), it has some nontrivial consequences. Labels are also nodes(almost) only placed differently. If you add draw
option to your node, you don't need to draw it's box additionally.
You can also pass regular options to the label node (because it's a node) as follows
\begin{tikzpicture}
\node[draw,minimum size=1cm,label={[align=center]below:unit\\cell}] (one){};
\end{tikzpicture}

If it becomes tedious to write complicated label codes just use the positioning syntax
\begin{tikzpicture}
\node[draw,minimum size=1cm] (one){};
\node[align=center,anchor=north] (lab) at (one.south) {unit\\cell};
\end{tikzpicture}
which leads to the same result. There are a few more ways of doing it but no need to complicate it for this simple application. You can find many examples here too by searching for positioning library use.
[text width=1cm]
but the question is not precise. You want multilines but where ... why\tikz{\draw (0,0)rectangle (1,1);}
?