Could a Roman have made it to or have been living in China or north-eastern Russia (Vladivostok direction) at the time? What about Japan or Australasian islands?
If nothing can be proven, what would the likely answer be?
I can't answer the actual question (furthest) but as a subset of your question: romans reached China in the 2nd century. (if i had to guess: for a normalish person India would be the furthest they could go: the Roman-Indian trade routes on the indian ocean provided persistent contact as opposed to the very rare meetings with china).
Now for China: In around 166 the Chinese recieved an emissary from Da Qin/Tachin aka "great Qin" aka Rome/Roman Asia in China via Vietnam. I learned about this from the Chinese side so i don't know if there were more travels we know about but i doubt they got much further.
If i was looking for a more complete answer i might look at any Romans possibly settling in India and then eastern indian trade routs. But i have no clue what that would turn up.
One reason contact was so limited was "Persia" (using generic term for long term point) had a clear interest in avoiding any direct trade/connections between Rome and China which would cut them out as the middle men on the silk road.