Rosh Hashanah, chapter two, mishnah 4. This mishnah spells out exactly where those mountaintops were located on which the torches and flares were lit, and what route the news of the sanctification of the new month traveled from Jerusalem onward.
The route of the torches - from where to where:
"MeHar HaMishchah" - from the Mount of Olives (Har HaMishchah is another name for the Mount of Olives), which stands just outside Jerusalem.
"LeSartava" - to a mountain called Sartava.
"LeGrofinah".
"LeChavran".
"LeBeis Biltin" - and from Beis Biltin they went no further, since from there on there was no need to continue.
"Molich u'meivi u'ma'aleh u'morid" - back and forth, up and down:
The man stationed at Beis Biltin would wave his torch back and forth, raising it and lowering it, while looking out over what the mishnah calls "golah" - which actually refers to the city of Pumbedisa in Babylonia. He would keep doing this, "ad shehu ro'eh es kol hagolah lefanav kimedurah shel eish" - until he saw the entire exile before him like one great bonfire of flames. Here too the intention is not the entire exile, but Pumbedisa.
And how did that bonfire come about? Every single person, upon seeing the torch on the mountaintop, would take a torch of his own and climb up to the roof of his house. Hundreds and thousands of people went up onto their rooftops and waved their torches, and when the man at Beis Biltin saw this, he knew that from here on the message would go out to all the communities of the exile, and everyone would know when Rosh Chodesh fell.
In summary: in this mishnah we learned the chain of torches on the mountaintops - from the Mount of Olives to Sartava, to Grofinah, to Chavran and to Beis Biltin - and what the man standing at Beis Biltin did, waving his torch back and forth, up and down, until the whole exile appeared before him like a bonfire of flames, thanks to the torches that the people of Pumbedisa waved on their rooftops, and from there the news of the sanctification of the new month went out to all the communities of the exile.