Book translation: when I go anywhere, I always carry my mobile phone.
Reasoning: the place is denoted by
どこ, which is a interrogative word and, because of that, it can follow も to mean 'all', so
どこもに行く means 'to go anywhere'. However, I suppose 'anywhere' is not a place you can go.
Reasoning: どこにも is an adverb, meaning 'anywhere' if used with a positive verb.
I'm also not sure why
どこに行く時にも is grammatical to start with. That's probably why I asked this question.