Is there a Grothendieck topos $F$ such that, for any Grothendieck topos $E$, the category of geometric morphisms $$E\rightarrow F$$ is equivalent to the category of locales internal to $F$?
I suspect that such an $F$ doesn't exist, because the definition of locale doesn't look to me like it can be formalised as a geometric theory. But it would be nice if there was such a classifying space, since the locales internal to a topos are interesting objects. In particular, if $X$ is a locale then the locales internal to $\mathrm{Sh}(X)$ correspond bijectively with bundles over $X$, i.e. pairs $(Y,f)$ where $Y$ is a locale and $f:Y\to X$.
Points of a topos are always accessible, the categories of frames or locales are not.