I have used Kilikia bus station to travel from Yerevan to Tbilisi using minivan (marshrutka), but seems you can get from Kilikia to Istanbul (Turkey), Tehran (Iran) or Moscow (Russia), take in note those will be very long trips (starting 40 hours) and I would rather prefer to fly instead of traveling such long distances by bus.
I reserved a seat a day before by calling to firm in Yerevan - Tbilisi minivan (Read more:Tbilisi - Yerevan transfers by taxi car ). Cost for Yerevan - Tbilisi minivan (7 seats in comfortable Mercedes Benz minivan) is 8,000 AMD (USD 17) (As of March, 2016). Minivan was leaving at 10:30. I don't know for sure precise departing times, but they for sure have many daily routes to Tbilisi, like at 9:00,11:00,13:00,15:00 and 17:00. It took about 5 and half hours to reach Tbilisi (Avlabari metro), with a longer (about 20 minute stop) at some gas station near Georgian border, and about 15 minutes at Sadakhlo Georgian/Armenian border for passport checkup.
Of course local (domestic) Armenian routes are served from here as well. They should be really cheap also.
Kilikia bus station is located pretty close to city center, just next to Ararat brandy factory. If you will take taxi from city center, you will be charged the minimum 600 ADM fare (it's really close). I took a taxi from our hotel and gave him a tips - 1000 AMD (equals to about USD 2.00). Taxi's are cheap in Yerevan.
Kilikia bus station in Yerevan
The station is not in the best shape, seems last time has been reconstructed back in Soviet days. Mostly marshrutkas are leaving from here.
At Kilikia Bus station
Private drivers and marshutkas.
Local routes served from Kilikia bus station