Athens is one of the most accessible destinations all year round. During summer, the temperatures are quite high, but in spring and autumn, Athens is very friendly. Many tourist attractions have lower prices between November and March, but there are also free tickets on certain days of the week. Here are 10 free visits:
1. When you say Athens, you say Acropolis. Free admission days are: March 6, April 18, May 18, the last weekend of September, October 28, every first Sunday of the month from November 1 to March 31. Young people up to 18 years old have free entry.
Even if you do not find a day with free access, I think that the 20 Euro (1.04-31.10) or 10 Euro (1.11-31.03) for access, will be a well-deserved investment to see one of UNESCO’s world objectives. Careful! Acropolis is very visited all year round, queues are made both at the entrance and at the purchase of tickets; from experience I recommend visiting in the early hours of the day or buying tickets online. A! and get comfortable shoes because the stones and the ascent can pose some problems. Schedule: Mo-Su: 8-20 (1.04-31.10) and 8: 30-15 (1.11-31.03).
2. Changing the guard at the Parliament Palace, on Syntagma Square. On Sunday at 11 am, soldiers known as “Evzones” march from the palace to the Tomb of the Unknown Hero on Vassilis Sofias Street.
3. A walk in the National Garden, located near the Parliament Palace. Queen Amalia is the one who created this oasis. Here you can see turtles, swans, ducks, rabbits and a few other animals as a mini zoo is housed here.
From place to place there are busts and sculptures of some well-known Greek people. You can buy gyros from Syntagma Square and even have a picnic here.
4. A pedestrian tour of the center of Athens costs nothing. You can visit the Psirri neighborhood where it is very good food, Monastiraki Square (don’t miss a tour of Adrian’s Library – it can be seen perfectly from the outside), Plaka neighborhood with its street paintings. Anafiotika area is a must see if you are in Athens. It is a small neighborhood built by workers coming from the islands. They wanted to recreate the corner they were used to live; that’s how this neighborhood appeared. When you enter Anafiotika it is like walking in the picturesque villages of Greek islands. You can visit Athens through a free guided pedestrian tour, the details of which can be read here.
6. Climb the two hills of Athens that offer great panoramas: Filopappou Hill and Lycabettus Hill. The first gives the perspective of the city, including the Acropolis, to the Saronic Gulf; at its peak is the monument of Filopappos from 115 AD. raised in honor of the benefactor of the city, Julius Antiochus Filopappos. Lycabettus Hill offers a 360 degree panorama and can also be reached with the funicular on Aristippou Street. Price: 5 Euro / one way. 7.5 Euro / 2 ways.
Upstairs is the church of Agios Georgios and a café, and also an absolutely wonderful panorama. It is said that this hill was the hill of wolves, because lycos 
means wolf in Greek. I preferred to go up by funicular and went down hill through the pine forest that surrounds the hill where I only met dogs with their owners and pots of water for thirsty animals. By the way, it seemed very nice that people leave vessels on the street with water for stray cats.
6. Visit the numerous antique fairs that are near Monastiraki Square. Also here is the Varvakios Square where fruits, fish and meat are sold.
7. Admire the many artifacts found by archaeologists on the subway stations. They are located in Syntagma, Panepistimio, Acropolis and Monastiraki stations.
8. Visit the Museum of Instruments that gathers 1200 Greek instruments from the eighteenth century to the present. The museum has free admission. The program is Tu-Su: 10-14, We: 12-18, Mo: closed.
9. Also free of charge is the Municipal Art Gallery in Koumoundourou Square, which houses works by artists who have had a profound impact on the history of Greek art.
10. Benaki Museum has a free entrance each Thursday in the main building, in the Kolonaki neighborhood located near Syntagma Square and the Parliament Palace (the museum has several offices). The cornerstone of the museum was laid by Antonis Benakis, a collector and benefactor of the art.
The museum houses art pieces from the Neolithic period to the present. It is one of the most representative museums that can be visited in Athens.
11. Bonus, on a street that connects the Acropolis with Agora, lies the oldest house in Athens, 
which can be visited for a modest donation, one offers as much as he or she considers. The villa is on a street full of souvenir shops and is on two levels. It seems that this was the home of Saint Filofteia. .
To visit the important sights of Athens, I recommend the combined ticket for archaeological sites. It costs 30 Euros, has a validity of 5 days and offers discounts or free of charge at the entrance to the most important sites; this ticket is worth buying if you intend to visit more than two of the 7 included places (Acropolis, Old Athenian Agora and Museum, Kerameikos and Kerameikos Archaeological Museum, Temple of Olympian Zeus (Olympieio), Roman Agora and the Wind Tower, his Library Adrian, Aristotle’s School (Lyceum)), and if you come in November – March, then some tickets are already reduced and this ticket is no longer needed. Online tickets can be purchased here.
You can go by subway to the port of Piraeus, to visit this part of the city. In the hot season, visit the beaches near Athens, you can take a dip in the sea.
Of all the places where I ate gyros, here was one of the best, and the price was 2.5 Euro / piece.
What other interesting places have you found in Athens?