Here are a few ideas for things to do in Athens for 3 days while spending 500€:

1. Visit the Acropolis and the Parthenon: This is one of the most iconic landmarks in Athens and a must-see for any visitor. The Acropolis Museum is also a great place to learn about the history of the ancient city.

1. Explore the Monastiraki Flea Market: This is a great place to find unique souvenirs and gifts. You can find everything from traditional Greek pottery and jewelry to vintage clothing and furniture.
2. Take a food tour: Athens is known for its delicious cuisine, so a food tour is a great way to sample some of the best local dishes. You can find tours that focus on specific neighborhoods or types of cuisine.
3. Visit the National Archaeological Museum: This museum is one of the most important archaeological museums in the world and has an extensive collection of ancient Greek artifacts.
4. Take a day trip to Cape Sounion: This is a popular day trip from Athens that takes you to the southernmost tip of the Attica peninsula where you can visit the Temple of Poseidon and enjoy the beautiful views of the Aegean Sea.
5. Visit the ancient Agora: This is a great place to learn more about ancient Greek culture and history, and it’s home to several important archaeological sites, including the Temple of Hephaestus and the Stoa of Attalus.
6. Visit the Hadrian’s Library, one of the most impressive ancient monuments of Athens, and learn about the city’s history, culture, and art.
7. Enjoy a night out in Gazi area, which is a lively neighborhood full of bars, clubs, and restaurants.
8. Take a stroll around the historic district of Plaka, which is home to many charming shops, restaurants and beautiful neoclassical buildings.
9. Finally, take a relaxing stroll along the seaside promenade of the Athens Riviera, which is a great place to enjoy the fresh sea breeze and lovely sunset views.

Please note that the prices might be different depending on the current situation and the date of the visit!