As mentioned there are plenty of options for people looking for day trips from Yerevan. One of them is the so called Garni-Geghard trip which combines a Hellenic Pagan Temple from the first century with a much more impressive Monastery called Geghard (or Geghardavank) meaning the Monastery of the Spear, as the spear that killed Jesus during the crucifiction once was kept there.
To get to Garni you can take a mashrutka from the Gai Station in Yerevan for as little as 50usd cents for the 30km long ride. The entrance is also very cheap if you are a student (20cents) whereas others have to pay 3 dollars to get in. At the site there is a pagan temple from the first century, but the heavy restoration makes it look fairly new. A visit is not really neccessary.
Second up was the Geghard Monastery which was way more impressive. Built in the 4th century in the mountains together with lots and lots of caves there is plenty to do to keep you occupied for an hour at least! There are trails leading into the woods where you will find trees with cloths wrapped around them, which apparently make wishes come true, and if you continue furthee up the mountain you will get exceptional views of the monastery which 99,9% of the visitors will not see.