Here are some suggestions & tips for you.
Get an early start in the morning. Start the day with a full breakfast in, although Greeks dont do that! Nestorion Hotel, Pentelis 8, Palaio Faliro, Phone: +302109425010 e-mail: info@nestoriohotel.gr http://www.nestoriohotel.gr
MORNING
1/ If you are interested in history, take a historical walking tour and visit all main attractions of Athens (http://www.theacropolismuseum.gr/). See Acropolis & comprehend its history with a licensed tour guide (in Greece only licensed guides are authorized to give you a guided tour). There are many interested monuments in Athens and many you can see.  http://www.benaki.gr/
2/Hop on-hop off an open bus and enjoy a nice drive around the city. Need something more active? Rent a bike and see Athens with a different perspective.
http://www.city-discovery.com/greece_athens_tours/tour.php?id=4936
3/History is your gem? Are you more of a foodie? Then sample & learn all about Greek food culture & products.
4/Want to relax? Swim at turquoise thermal waters of the spectacular Vouliagmeni Lake http://www.limnivouliagmenis.gr  or take the one day cruise from Faliro to three beautiful islands http://www.olympiccruises.gr/ or visit Marathonas dam. http://www.fragma.gr/
5/Take one day tour outside Athens such as an excursion to Delphi or Argolis or even a multi day tour on the islands or a multi day tour in the mainland.
LUNCH TIME
6/Time to take a break, enjoy lunch, recharge your batteries before you go on exploring the city. Whether you want to have a snack or lunch, traditional or modern, Greek or international ask for some options in the center of the town. There many nice restaurants and taverns in Athens with excellent food. http://www.alexandra-restaurant.gr
AFTERNOON
7/How about shopping? Athens has becomes a shoppers paradise. Large shopping malls prestigious department stores, famous cosmetic brands, well known international brands but also small local stores (http://www.pandrossoustreet.com/), Greek Brands, handmade leather goods, jewelry, souvenir shops, traditional products and many more. Find the deal gift for yourself or your dears ones.
EVENING – NIGHT
8/The Mediterranean diet is a modern nutritional recommendation inspired by the traditional dietary patterns of Greece, Southern Italy and Spain.
Take a hands-on Cooking lesson & Dinner (*), prepare your own Greek food, learn secrets of the Mediterranean diet, take home with you authentic Greek recipes & have cooked yourself or participate in a wine tasting & try some excellent Greek wines.
9/ Maybe Athens is the perfect city to find your other half. http://www.whenthemusicstops.gr
10/Athens is a vivid city, with many restaurants, bars, concert halls, open air festivals and a lot of Greek music. Let your self experience the Greek way of fun!.
(*) Athens Cooking Lessons Starts at  5:30 pm & takes place Monday to Thursday, 63€ for adults. Tel. +302108847269 http://www.athenswalkingtour.gr