I'd use the verb in number 2.
"We parted." or "We parted at the train station." or "We parted after dinner."
past tense: parted; past participle: parted
(of two things) move away from each other.
"His lips parted in a smile."
leave someone's company.
"There was a good deal of kissing before we parted."
synonyms: leave, take one's leave, say goodbye/farewell/adieu, say one's goodbyes, say/make one's farewells, separate, break up, go one's (separate) ways, take oneself off, set off, be on one's way, go, go away, get going, depart, be off.
'We split up' is commonly used for relationships that ended.
'We left each other' is vague. If there are three people at the train station, then the two boarded and the third didn't, the third person may say that the other two 'left' and he/she was 'left behind'.