Athens is an ancient city and full of places to discover. So often it gets rather overlooked as many tourists opt to head straight for the islands. If you have the time, even just a day in the city is certainly worth the time before you head out to Santorini or Mykonos or any of the other gorgeous islands. While in Athens (especially if you have only a day or two) I would highly recommend staying in the neighborhood known as Plaka. It is a pretty area full of winding roads and delightful tavernas. It is also quite literally at the foot of the Acropolis so you will easily be able to walk up to see the sights (and they are certainly worth it.)
In Plaka there is a lovely little hotel called Home and Poetry that is an ideal place to stay when in town. It has a beautiful roof top garden with a view of the Acropolis where they serve breakfast in the morning as well as drinks until midnight. All of the 16 rooms and suites are named after famous poets and can sleep from one to four guests. There is even the Skylight Suite on the top floor which is quite spacious and features not only accommodation for four guests but also two separate seating areas and is essentially under the eaves of the building so has several skylights instead of windows.
Interior aside, you really cannot ask for a hotel in a better location. It is only a very short (and beautiful) walk from the Acropolis and right in the middle of Athens' most scenic neighborhoods that is simply bursting at the seams with delicious places to eat. You can even easily pick out the hotel's roof top garden during your walk around the Acropolis! There are endless little shops to explore as well as lovely spots to sit under an olive tree with some ice cream on a hot and sunny day. It is also fantastic to wander around the neighborhood and catch stunning views of the Acropolis lit up at night - it is a sight absolutely not to be missed when in Athens. A short walk from the hotel also takes you to Areopagus Hill which offers spectacular views of the Acropolis day or night - but be careful! The marble is very polished and slippery!
While in Athens there are much larger and fancier hotels with a number of amenities - Home and Poetry is lovely and intimate, giving you the feeling that you are living like a local. If you want a spa or a gym (perhaps a Finnish sauna?) then there are certainly more suitable options for you in Athens, but for the classic Athenian hospitality in a wonderful location, Home and Poetry is the place for you.