。
She went to either London or Paris.
Literal
[topic-は] London [or-か] Paris [genitive-の] either-どちらか [to-に] went.
~か~のどちらか is a useful template for 'either X or Y' when only two options are involved. か here is the alternation particle ('or'), distinct from sentence-final か (question marker). どちらか literally 'which one (out of two)' picks out one of the two paired alternatives. The whole noun phrase A か B のどちらか packages 'one of A or B' as a destination, then takes に for the direction.