Yerevan was very much different than both Baku and Tbilisi. It has been seat of an empire more than five times its current size and the city boasts of soviet style monuments and buildings on the scale of those in Moskva and Minsk.
One of these buildings is the Cascade. A massive staircaise decorated with flowers that hosts many floors of museum and art objects connected by series of escalstors. From the top you can get a good view of the city, and particularly the opera house with is at the end of one of the main streets called Northern Avenue.
The daily fountain show with music outside of the Historical museum
The city center has a circular shape, with the bus roads and parks being curved around the main plaza called Republic Square. One of the main attractions is the brandy factory museum, but as I had not pre booked a tour I didnt get to see it. Another great museum was the free Armenian Genocide Museum which was probably the best museum I have ever visited! I had no clue about the scale of the massacres of Armenians during the Ottoman empire in the beginning of the 1900s before I went there.
There are also lots of stuff to do not far from the capital. I went on day trips to the Geghard Monastery, Garni Pagan Temple and the Zvartnots Cathedral outside of the old capital Vagharshapat- the latter two looking more like East Roman ruins than anything else. In the background of Vagharshapat I could also see the highest Mountain of Armenia, Mt. Ararat but unfortunately this could not be as easily seen in the photos that I took.