I think Georgia and Armenia are an excellent choice - both countries are fascinating and I’d say Tbilisi is one of my favourite destinations in the world.
Yerevan is a nice city to walk around with interesting architecture and an interesting Metro. I stayed in the Ibis which was very Central and I could walk almost everywhere I needed to go.
You could do a day trip to Lake Sevan. The lake is picturesque, there’s the famous Brutalist Writer’s House and a Church / Monastery. The scenery en-route is quite nice too.
You could also do a day trip the other way to Jermuk. It’s a Soviet style spa town. The scenery en-route is beautiful (winding mountain roads, a gorge...etc). There is not a huge amount to do when you get there other than view the waterfall and wander around town - the journey is worth it though. It’s also interesting seeing all of the Iranian trucks that have just come across the border (some are very old Macks).
Tbilisi - and Georgia in general - is very interesting. I have always stayed in the Ibis Styles which has a great location (there’s a Crown Plaza nearby too). There are lots of restaurants in the area and Liberty Square). There are traditional touristy things to do in Tbilisi but some companies also offer Brutalist Architecture/ Soviet tours where you can see some of the legacy of the Soviet times - which I find quite interesting.
There are numerous day trips you can do. I hired a car and drove to the Soviet monument in Gudauri stopping at various sites en-route. The drive in the mountain roads is beautiful. Companies offer this tour if you don’t want to drive. You could also go to Borjomi (a spa town - quite nice but the drive there is a bit boring), Gori (to see the Stalin museum - although I’ve never managed to do this). You could also do a day trip to Chiatura - a former Soviet mining town for magnesium. This was fascinating although it’s not so interesting now the Soviet-era cable cars have stopped working (apparently they’re dangerous!)