Simon essentially answered the question already, but I will expand some of the parts that may not be clear to the experts. Sketches of an elephant is a good reference for everything I am going to say.
Construction. (From prebounds to localic geometric morphisms) Let $\mathcal{E}$ be a topos. A prebound $e \in \mathcal{E}$ is an object such that the subobjects of its finite powers $m: a \to e^n$ are a generator for the topos. Such an object always exist and can be obtained by manipulating a generator. Given a couple $(\mathcal{E},e)$ where $\mathcal{E}$ is a topos and $e$ is a prebound, we can construct a localic geometric morphism $$f_e: \mathcal{E} \to \text{Set}[\mathbb{O}]. $$ Of course, this is the same of a cocontinuous left exact functor $f_e^*: \text{Set}[\mathbb{O}] \to \mathcal{E}$, which is the same of a lex functor $\text{Fin}^\circ \to \mathcal{E}$. The latter, is given by sending $n \mapsto e^n$. The geometric morphism obtained in this way is localic by definition of prebound. This construction appeared for the first time in Freyd's All topoi are localic.
Remark. If you think about it, I am just spelling out in categorical terms what Simon suggested in somewhat mystical language.
Remark (Morita-like phenomena). Notice that each prebound (and we can construct a prebound from any site) gives a different localic morphism, thus we have many localic representation for the same topos!
Theorem. There is a biequivalence of categories between the $2$-category of internal locales in $\text{Loc}(\text{Set}[\mathbb{O}])$ and the $2$-category of localic geometric morphisms over $\text{Set}[\mathbb{O}]$, $$\text{Loc}(\text{Set}[\mathbb{O}]) \leftrightarrows \text{Topoi}_{\text{loc} / \text{Set}[\mathbb{O}]}. $$
Def. The $2$-category WTopoi of well presented topoi has objects $(\mathcal{E},e)$ where $\mathcal{E}$ is a topos and $e$ is a prebound and morphism geometric morphisms whose left adjoint preserve the prebuound.
Theorem. There is a biequivalence of categories $$\text{Loc}(\text{Set}[\mathbb{O}]) \leftrightarrows \text{Topoi}_{\text{loc} / \text{Set}[\mathbb{O}]} \leftrightarrows \text{WTopoi}.$$
Remark. Of course, the WTopoi is not the same of Topoi but the forgetful functor WTopoi $\to$ Topoi is essentially surjective on objectd and on morphisms!