besides the obvious (Acropolis, Parthenon), what else do you recommend we do with 4 full days in Athens? and where should we stay? and where to stay by the airport (an extra night before we fly to Crete). any suggestions are greatly appreciated.
I'd definitely walk up Fillopapus, also known as the Hill of the Nymphs. IMHO the best view of the Acropolis is from there.
Also in central Athens Lycabetus has great views. It's the cone shaped hill with a small church on the top. Walk from Syntagma Square up through Kolonaki, the smartest shopping area in central Athens, and you can then get a funicular railway up to the top of Lycabetus.
Slightly further afield, but only on a local bus, I'd visit the 11th Century Monastery at Kessariani. Take bus 223 or 224 from Akadamias, behind the university, up onto the foothills of Mount Immitos. When the bus terminates you've got a 30 or 40 minute walk up to the monastery. Initially there's the road on one side and a cemetery on the other but once you've gone under the motorway you can cut up to the right on a footpath that takes you onto a flank of the mountain with great views over the city. There are picnic tables if you're so inclined. As the path reaches the top of the first hill turn left and walk parallel with, but above, the road you've left. After a while the path leads you back down onto the back of the monastery.
The Attalos is worth looking at as somewhere to stay. Not particularly atmospheric but the people are friendly, it's well located, and has a great roof garden
For somewhere smaller and less standard you might look at the Tempi
Take the funicular up Lycabettus Hill for a drink in a cafe overlooking Athens at sunset. Be sure to go to the National Archaeological Museum and the Benaki Museum. You can also take daytrips out of the city to Sounion Bay and Delphi, or to the charming little island of Hydra, which is close to Athens..
Near the airport is the St. Thomas B&B. They offer free airport shuttle (to and from) between 8 AM and 10 PM.
Another one is Peri's Hotel. They offer free shuttle from 7 AM to Midnight.
Just last weekend I met up with Greece travel partner and we reminisced about our stay in a pension that was located back behind the Hilton and not far from the American Embassy. It was used by visiting university professors. I can't find it, but had a great time searching for it on the web. But it did remind me that one of the great things to do is to go up to the top of Lykobettus. There is a funicular and the views are great. I visited Cape Sunion when I was in Athens the first time. It's out past the airport if I remember correctly. I know I got there by bus as I was 19 and carless at the time. Don't forget to see the national museum. Many of the artifacts from the archeological sites are in this museum and not on site or in a local museum. Don't miss the Agora at the foot of the Acropolis. Also, there are many companies that offer day trips to Delphi, Corinth, Mcycenae etc. By the way I found this site during my search for the pension.http://www.athensguide.com/ It looks really helpful to me.