The best area to stay in Athens is at THISEIO (map). This is a very romantic area, with the view of Acropolis. This location is very convenient with a a metro connection to everywhere. And it is also is very close by to the party area, only 15 minutes max walking or you can you with the metro.
If you visit Athens in mid summer, and want to stay more close to the beach, the P.Faliro area is a good place to stay. It's located next to the beach.
Glyfada is nice too, but it is located a 45 minutes bus ride away from the centre.
Hotel map of Athens
Check our online hotel map of Athens to see hotels and their actual prices on the map