A day in Athens having previously visited main sites

[RockingMyFiftiesNot]

We have a spare full day in Athens in October. We've been to Athens before and have visited the main sights & also visited Piraeus .
We are happy to have a relaxed day with lazy breakfast/lunch/coffee stops, but would like to explore the city a bit more, there must be loads we haven't seen! We enjoy walking and happy with parks etc.
We don't want to travel elsewhere, and unless it rains don't particularly want to be indoors.
Any suggestions for places that tourists don't usually visit / hidden gems etc. please? Am asking now as we may extend the stay there if we find there is much more still to see than we realised and I want to reserve hotel asap. I am Googling for ideas too but sometimes it's better to ask people who have been as the internets 'hidden gems' aren't always that great when you get there! Thank you

You may have already been there, but how about Mount Lycabettus, the highest point in the city?
It's decades since I was there but I remember the views.

Thanks @TreesAtSea. No we haven't, we discounted it thinking we'd get similar views from the Acropolis but was reading about it earlier and definitely think it's one to do.

A hopeful bump