The centre of Yerevan is quite developed, there's a lot of hidden little things to discover but yeah nothing to really explore. It's when you step out into the other districts that the history starts to open up: massive factory complexes in the south. The 50s smoke stacks and factories that are completely untouched just tucked away behind khrushchevkas. Also tons of little overgrown parks with old streetlights and monuments. I've been finding quite a few little gems around.
I know which swimming pool you mean, they're quite common once you step out of the city. I stumbled across one in Ejmiatsin behind the church. There's an even bigger one on the next town over from it near Metsamor. Such a strange thing to see in those towns. Which were once much bigger and had more life to them. Including cinemas and photography and various culture houses. The pools really are effective in showing how much things have decayed since the fall of the USSR. People once spent their days cooling off from the hot sun in those pools, and now what remains are crumbling tiles and concrete.
Most of these things I've found from just walking. I'll grab my camera and all my batteries and just walk through districts, between the buildings and through towns. Sometimes I'll spend some time looking at the maps and seeing if there might be anything interesting in certain towns or regions. Each of these pins is something I've found either on the map or in person.
Feel free to reach out if you ever decide to come back here, I'll be able to recommend some places :^)
RE: Nor Arabkir Park and WW2 Monument, Yerevan