trip Itineraray

Why don't you keep Athens for the end? This way, you wouldn't loose a night close to the airport.
Ideally, you would fly to Athens and fly the same night to Santorini, on the 16th. Sleep there 4 nights(3 full days which is good).
Then fly back to Athens.
What I suggest is take your car right away, drive south to the Temple of Poseidon(google it, it's an amazing site)
Then drive to Delphes. it's about 3 hours. If you find it's too much, skip the temple, or do it when you come back.
Depending on when you arrive in Delphes, you might need 2 needs. We arrived at the site at 9am and left at about 2pm. So I think I would go and see the temple, drive to delphes, take it relax, see the small city next to it.
Then visit Delphes the next day and in PM, go and see the Osios Loukas monastary which is fairly close to Delphes.
Leave next day aerly for a 3:30 drive to the Meteores. I left at 8, arrived around 11:30, lunched and spent the afternoon visiting.
It's tight, but you can do it. If not, relax there and stay one night and come back.
2 full days will be good in Athens.(or 3 nights). Then you can leave from there by taxi to catch your flight.
I haven't seen Hydra, but saw many sites around Nafplio, 2 hours south-west of Athens: Epidaure, Corinthia, etc.

I like you second alternative better than the first. Look at Peris hotel. Its about a 15 minute drive from the airport and they offer free shuttle service. Of course if you have a big budget you can stay at the Sofital which is at the airport. As I see it you have a total of 9 nights in Greece. So that is night 1.

Next morning fly to Santorini.
You might consider an additional night in Santorini. Flying on the 17 and returning on the 19 is really only a day and a half in Santorini.
You will still be jet lagged so spend the extra day relaxing and taking in the views. So that is night 2,3 and 4.
Santorini http://www.flickr.com/photos/stanbr54/sets/72157632154800782/

Now fly back to Athens and rent the car from the airport and drive to Delphi. This should allow you to arrive in the afternoon. Find a hotel, wander the village take in the amazing view down to the gulf of Corinth visit the museum and if you still have time visit the lower site. That is night 5

Next morning get to the site at opening. You will have it virtually to yourselves for at least tow hours until the tour buses arrive. Then you will be way up in the site and it will take about another hour before the crowds reach you. Leave by noon and drive to Meteora. Time you arrival late afternoon or better yet early evening. At this time the monasteries will be closed and the crowds will be gone. Take your pictures then because next day the tour crowds will be everywhere. Night 6

Determine which monasteries will be open the next day and get to at least the first one before the tour bus crowds arrive. This can be a long day so you might consider two nights at Meteora because it is a 5 hour drive back to Athens. night 7

Olympia Delphi Meteora https://www.flickr.com/photos/stanbr54/sets/72157645469717811/

Drive back to Athens for the end of your trip. You now have 2 nights for Athens before your flight home on the 25th. Nights 8 and 9. This plan gives you one extra full day in Santorini plus everything else you planned. Sequence is very important. You initial plan had to many trips into central Athens. Keep it to the end,

Athens http://www.flickr.com/photos/stanbr54/sets/72157632121475515/

Thanks you all for your reply. Much appreciate. More clarity. Couple of other questions, which one would be the best neighbor hood to rent airbnb in athens?

Thanks again
SC

Plaka is the central tourist area and there are some reasonable apartments there. The upside is that you are very close to everything but the downside is that it can feel very full of tourists and everywhere is a bit more expensive.

I'm actually in Petralona at the moment. It's more of a Greek neighbourhood and places are cheaper. It's a couple of stops on the metro to the centre though.

A good compromise might be Koukaki. It's just below the Acropolis but on the other side from Plaka. It's an up and coming area with some good restaurants but you can easily walk in from there.

Alan

Thanks ! Appreciate the reply

While the Monestraki, Plaka area would be preferred I recently read that the area of Koukaki has become very popular for owners renting their apartments on sites like VBRO and AirB&B. The area is not far from the Acropolis.

we just found an airbnb in koukaki for under $50 per night and the owner has a driver who will drive us to the airport for $38 in the middle of the wee morning hours for a 6 am flight.