We often (and with some justice) think of the Romans as a totalizing diplomatic force in their own region and beyond.
I'm curious, though, about whether or not there were cultures or commercial groups or anything that had heard of the Roman Republic or Empire, but which had never yet encountered that republic or empire formally. What was their view of this titanic political and economic entity? What did they hope to achieve from such contact?
I'm not an expert but a good starting point would be researching Chinese envoy Gan Ying. Here is an interesting article describing that he reached as far as Turkey and reported back to China about the Roman Empire.
http://www.ccta.me/2012/08/mark-shanenvoy-gan-ying-of-chinas-han.html
The first Roman Emperor Augustus wrote a personal journal at the end of his life. In it, he describes being "visited by envoys from the Rajas of India" or something of that effect.
Source: Excerpts of Augustus's account are in Ancient Rome: An Anthology of Sources by R. Scott Smith.