The nearest metro stop is Acropoli, about 2 blocks uphill from the Hera. Across the street from the metro is a block of tourist restaurants - don't go there! If you go downhill from the Hera a couple of blocks, you'll find a lot of restaurants, much cheaper and many more locals. BTW it's easy to get to the hotel from the airport using the metro.
The Acropolis Museum is behind that metro stop. It's worth a visit, but as Paul said, the National Archaeology Museum is the wow. However, for your first night, you may want to go to the Acropolis Museum since it's close. Whether you visit it or not, you can have dinner (reasonably priced) on the open balcony with a great view of the Acropolis. The Hera has a rooftop bar/restaurant, the view isn't as good and it's indoor with wall-to-wall windows.
Definitely go to ManiMani for a great dinner. I'd have gone more than once if I'd known how good it was.
I think you're taking on too much on Saturday. It will be hot and there's very little shade. I was there 2 years ago and used the RS 2016 guide, which said you could exit the Agora at the foot of the Acropolis. There was a small exit gate that was unkempt and padlocked. Also Athens is hilly and you'll be going up and down in the heat. I would try to visit the Acropolis first thing in the morning, whichever morning you choose.
There is a special changing of the guard ceremony on Sunday morning at Syntagma Square at 11.00, with lots of extra pomp and a marching band. It starts about 10.45 and you'll want to be there earlier to jockey for a position to stand and watch. Of course, you can see the ordinary changing of the guard every hour on the hour 24/7. And on the half-hour the guards rotate positions.