The CharIndices iterator has a field internally called front_offset, that I think would be very useful to have access to.
You can already do something like 'char_indices.next().map(|(offset, _)| offset)', but that is wordy, in addition to not handling the case where the iterator has ended, where you'd want the offset to be equal to the length.
I think it would be an easy and quite handy addition to add a method to CharIndices, maybe called 'offset' or something, that just gives back the starting offset of the next character.