Once you get tired of visiting similar spiritual spots in Yerevan, namely churches, which there are many of and some are pretty old, you can then turn to the only active mosque in Armenia known as the Blue Mosque. It was completed in 1765 and is currently one of the few old buildings in Yerevan.
During the Soviet times it acted as the History Museum of Yerevan. But then, after Armenia’s independence, it was renovated with the support of the Iranian government and again started working as a mosque. Nowadays, especially during the religious celebrations, there is a great flow to this mosque, of Iranians in particular.
Inside some of the halls there are exhibitions from time to time, usually on Iranian art and crafts. In one of the halls there are also free classes of the Persian language. I once tried starting the classes and even learned a few letters, but then had to give up because of issues with my schedule. I sometimes enter this place to walk around and sit here. There is no restriction on that. And while it is located right next to a busy avenue, it is calm and quiet inside.
For more details about this mosque and its history, have a look at this video.