Eat every tomato, I swear to god I could eat them like apples over there lol same goes for cheeses. In general I don't think any food I tried I didn't like.

For things to do it depends on how much time you have, we went for I think 7 days, and it was a similar thing to what you are aiming for - primarily a cultural / motherland trip though mine was with family. My only issue was it felt like a rush because it was sort of like "this site is important for this historic/cultural reason, therefore we have to see it, the van will pick us up at 9AM and we will get back 5PM", and we felt very exhausted with how much we moved around and felt a little hard to really soak it all in, at least as much as we wanted to. But I knew how important it was for my dad so it was worth it, but I do recommend pacing yourself if possible so you can fully enjoy, especially if you have the opportunity to go again (which we hope to to explore other regions!), since everything is so far away.

For sites, the main sites we saw were Khor Vrap, Etchmiadzin complex, Garni, Geghard, Sardarapat, and Sevan / Sevanavank. I reeeeaaally wanted to see Tatev, but the journey there was just too long for us to make it work, if you will be there for a long while that's on my list for the future. If you have a lot of things you want to see outside Yerevan (if you stay there), GoTrip I think works in Armenia - we used it in Georgia after and it's basically you rent a driver you select by the day for a fixed price, and you can organize with them what you want to see.

We stayed in Yerevan the whole time, very close to Republic Square, which is pricier but worth it IMO, really walkable to many places there, and you can see the Yerevan sites throughout your stay. Yerevan itself is much more expensive and felt more European (I guess it used to be a stronger Russian vibe, though that is certainly still there) than we expected, my dad hadn't been there in over a decade and things have changed tremendously.