Whenever you book a holiday to Athens you will no doubt be offered a number of tours as an option. Most are operated through travel agents and hotels by GO Tours, a local operator who have been in existence for many years.

There is a one day island hopping tour. This is by bus transfer to the ferry port then you are taken to three different islands, all fairly close to Athens port but do expect a good 12 hour day trip here. Firstly it's time for photos as you board (optional extra) and all drinks are also extra at higher prices than you would expect so take bottled water with you. On board, there is a great atmosphere with Greek dancing lessons, a good, although basic, set three course meal and a chance for some for the best sunbathing as you sail gently between the islands. Port stops one and two are mainly for souvenir purchases and photo opportunities with local donkeys and amazing scenery including harbours where the ferry dominates the whole harbour and puts the size of these little islands into real perspective. Stop three after lunch is where an option tour (20 EUR) takes you by bus on winding hill roads to a picturesque monastery built in gold and marble followed by an included trip to try the local drink and taste the seafood. The day trip isn't cheap and once you have added extras in it becomes costly yet it is a full 12 hour day and well organised with nothing to plan. Just beware of the illegal immigrants at the main harbour who do hassle you to buy copy sunglasses etc. They were swearing at tourists who declined to purchase and apparently the way to stop them is to ask if they have a license to trade on the port.

Another way to see the Greek Islands on a day trip is to charter a boat. There are many local charter companies who operate out of Athens, and there are some larger global charter companies who work with the local charters. Renting a private boat is a great way to explore the Greek Islands all in your own time. You don't necessarily need a licence to rent a boat, and it can be a lot cheaper than you think, depending on how many people are on the boat. Some charter companies include:

Zizoo - a global boat rental platform who work with charters in Athens

Sail Greece - who operate out of Athens 

MG Yachts - who also charter boats out of Athens 

TigSee - a Seattle based travel brand specializing in custom vacations to Greece (including Athens and island hopping).

Yacht Charter Greece - Yachtsailing charters in Greece. Based in Alimos marina offering mainly in a weekly basis cruises around the greek islands.

Another tour is the Athens City Tour. Taking in the main attractions including the original Olympic stadium, temple of Zeus and the Acropolis, the guide will give the tour in English. Do be prepared for a lot of energetic walking however as some of the attractions are up a couple of hundred steps.

Incidentally, you may also find in the Acropolis bus station a number of locals selling fabrics and tablecloths. It is well worth bartering politely here and aiming to pay around 1/3rd of the starting price, especially as the quality can be outstanding.

Should you be on the Acropolis tour and need refreshments, walk down past the bus station just a few metres down the hill along the parade of shops and you will find some local cafe's. There is also a further cafe, post office and souvenir shop halfway up the steps to the Acropolis. 

Note that you can do some of the tours on your own. Dolphin ferries offer island hopping from the port, water taxis also go between the islands. One ticket for the main attractions offers you access to a number of options from entry to the temple of Zeus to the Acropolis and lasts a few days, so if you plan your museums, attractions and routes well, you could find a less organised pace by using local taxis, trams and the general public transport network.

Check out the guide sellers at the temple of Zeus. For 10 EUR they provided an Athens guidebook, a monument and historical guide and postcard collection of the main attractions. This alone is enough information to plan a complete sightseeing tour.