Ooh we LOVED Athens! Agree with all of the above, plus would recommend going to the Stavros Niarchos Foundation Cultural Centre. It’s slightly out of town but there are bus/tram routes. I want to say don’t google it because we came across it without any idea and we were AMAZED; and actually went back twice in the 10 days we were in Athens. Absolutely stunning, and completely free to walk around. If there’s an event on even better, as those are free as well.
There’s a multi ticket you can buy that will get you into 7 of the ‘big’ ancient sites including the Acropolis; which was well worth it IMO - Aristotle’s School was a bit of a let down but everything else had enough old ruins to keep it interesting, plus we’re different enough from each other to not be too repetitive!
If you’re there on a Wednesday (?) evening go to the Observatory and they do an English tour - lovely old building with lots of history, plus you get to look through the telescope!
Agree with looking at bike/walking tours - that was how we discovered the cultural centre.
The Gas Works is also really interesting and I think was only a couple of Euros for a self-guided tour - it’s also an arty events space if you're Into that sort of thing.
We also did a maritime museum which had some really interesting stuff in it (though a bit crammed and disorganised!
It was a bit of a way on the tram line, but we also went to the Sea Turtle rescue centre which was small but interesting, and it’s a good charity to support.