Paxos is a lovely little island to the south of Corfu, ideal for a quieter and more relaxing Greek holiday because there's not much else to do other than swim and enjoy the beaches (though there are no sandy beaches), walk in the countryside, and eat and drink in some very good restaurants.
The largest town and capital is Gaios, with hotels, other accommodation, and some excellent restaurants, although these can be expensive by Greek island standards. Paxos attracts a number of upmarket holidaymakers, and many hotels and restaurants are geared more to these people who have a little bit of money to spend.
At the other end of the island is Lakka, connected to Gaios by the only main road on Paxos. Lakka is a small town/large village with accommodation choices, good eating, a couple of OK pebble beaches, and a good base for anyone who likes walking holidays.
The other main village on Paxos is Longos or Loggos, a really pretty fishing village with some very good restaurants around the port, making for the perfect romantic place to spend the evening.
Paxos is a tiny island and does not have its own airport. The nearest major airport is on Corfu, well served by flights from Athens and by holiday charter flights from all over Europe in the summer. The best way to get to Paxos is to buy a cheap ticket on a charter flight to Corfu, and then take the ferry from Corfu Town to Paxos.
Some package holiday companies charter their own boats to take their guests from Corfu to Paxos, while others use the regular passenger ferries. In the summer there is a fast daily hydrofoil service from the port at Corfu Town to Gaios, the main town on Paxos. There are also private sea taxi services between the two islands, and a car ferry service that links Paxos with Igoumenitsa on the Greek mainland, across from Corfu.
Ferries in Greece has an excellent and very thorough website where in addition to checking ferry schedules and times, you can also book tickets and get lots of useful information about travelling by ferry in Greece.
This Athens dining guide doesn't list restaurants but gives practical advice on types of eating places, tipping, hotel breakfasts and picnics.
Spetses in the Saronic Gulf Islands of Greece is an easy day trip from Athens and has some good beaches. This page gives details of ferries and what to do.
Athens Airport hotels include the luxury Sofitel at the terminals, Holiday Inn near the airport, and others close by like the Hotel Pantheon.