There are far too many inaccuracies told about this tower.
For a start, it is not in the ancient Agora of Athens. It is in the Roman Forum nearby. This is a completely separate area today and it requires a separate entry fee.
Next, it does not have sculptures of the six wind deities on its sides, because the building is OCTAGONAL (which means it has 8 sides) and there is a frieze around the top of the tower walls depicting the eight wind deities in marble. They are:
Boreas (N), Man wearing a heavy cloak, blowing through a twisted shell
Kaikias (NE), Man carrying & emptying a shield of small round objects
Euros (E), Old man wrapped tightly in a cloak against the elements
Apeliotes (SE), Young man holding a cloak full of fruit and grain
Notus (S), Man emptying an urn and producing a shower of water
Livas (SW), Boy pushing the stern of a ship, promising a good sailing wind
Zephyrus (W), Youth carrying flowers into the air
Skiron (NW), Bearded man with a bronze pot full of hot ashes and charcoal
Below each representation is a vertical sundial.
On the roof was a triton (male equivalent of a mermaid) acting as a weather vane, and pointing in the direction from which the wind was blowing.
Finally, some say we do not know what this building was used for. Wrong again! It was called the Horologion of Kyrrhestos and inside it was a public water-clock (or clepsydra), driven by a stream flowing down from the Acropolis. This water-clock was built (so ancient writers like Vitruvius and Varro tell us) by Andronicus of Cyrrhus around 50 BC, at a time when water-clocks were quite well-known to Greeks and Romans, and large public ones had been built elsewhere in the ancient world ... but they were uncommon. The city of Alexandria (in Egypt) was said to specialise in building them, and Andronicus is said to have trained there.
The only real mystery here is how the Athenian Horologion survived so well - and the answer may be that it was useful to whoever was in power over the ages, and owes its preservation to that fact. In the early Christian period, the Tower of the Winds was converted into a church. Later on, the Ottomans used it for various purposes (some say the Dervishers used it, but it is hardly big enough to whirl around in!). It gradually became covered with dirt and debris that accumulated over the centuries, until it was excavated by the Greek Archaeological Society around 1837-1845. Modern restorations took place throughout the 1900s.The Triton and water-clock have long gone. The wind dieties and sundials remain. Greece even issued a set of stamps with their images some decades ago, and these can sometimes be purchased at shops in the Plaka nearby. My friends Cas and Liz bought me a set while I was there.
Is it worth a visit? Absolutely! You can see it well enough from outside the fence, but the Tower and the Roman Agora in which it stands are interesting to walk through if you like to walk through history. The door giving entry to the tower is sometimes not open, but it has glass panes in it, so you can have a look inside the tower (though there is not much to see today.)
However, being up close to history is always a worthwhile experience. Go for it.