Arrival by train
The train station is quite a distance from the center. Erzincan has nothing to offer to the tourist, so it'll be most likely only a transit town.
From here, you can either go further east to Erzurum and Kars, but this way you will miss the beautiful monastery of Sumela near Trabzon.
Other option is to go to Trabzon which is quite a rough road
through the mountains. You need to get a taxi to the busstation, try to share it with other passengers.
I think it's not advisable to take the night bus. First of all the road was a track road, and secondly you would leave at 8 pm and arrive at 3 am, although it can also take 9 hours instead of 7 hours. I took the morning bus leaving at 7.30 am.
Go to Trabzon page