Yes, this is definitely a Greek tradition, a New Year's bread called vasilopita
Vasilopita (Greek: Βασιλόπιτα, Vasilópita, lit. '(St.) Basil-pie' or 'king pie', see below) is a New Year's Day bread or cake in Greece and many other areas in eastern Europe and the Balkans which contains a hidden coin or trinket which gives good luck to the receiver, like the Western European king cake. It is associated with Saint Basil's day, January 1, in most of Greece, but in some regions, the traditions surrounding a cake with a hidden coin are attached to Epiphany or to Christmas. It is made of a variety of doughs, depending on regional and family tradition, including tsoureki.
According to the article, the coins at one point were often quite valuable...
In older times, the coin often was a valuable one, such as a gold sovereign. Nowadays there is often a prearranged gift, money, or otherwise, to be given to the coin recipient.
Provided the coin is cleaned before being inserted into the dough, I don't know why it wouldn't be safe... coins aren't generally made with dangerous metals like lead and gold coins, as mentioned in the quote above, would be perfectly fine.
You don't say where you get "nickel" from... Greeks are on the Euro and I don't believe they use the term "nickel" for a five cent coin. They did have a five-cent drachma but it and other modern coins were made of cupro-nickel, a combination of nickel and copper, while others are made of aluminum or silver.
The first issue of coins minted in 1954 consisted of holed aluminium 5-, 10- and 20-lepton pieces, with 50-lepton, 1-, 2-, 5- and 10-drachma pieces in cupro-nickel. A silver 20-drachma piece was issued in 1960, replacing the 20-drachma banknote. Coins in denominations from 50 lepta to 20 drachmae carried a portrait of King Paul (1947–1964)
The coin is symbolic for religious reasons. Here's the story as related on a religious site:
One year, during a time of terrible famine, the emperor levied a sinfully excessive tax upon the people of Caesarea. The tax was such a heavy burden upon the already impoverished people that to avoid debtors' prison each family had to relinquish its few remaining coins and pieces of jewelry, including precious family heirlooms. Learning of this injustice upon his flock, St. Basil the Great, the archbishop of Caesarea, took up his bishop's staff and the book of the holy Gospels and came to his people's defense by fearlessly calling the emperor to repentance. By God's grace, the emperor did repent! He canceled the tax and instructed his tax collectors to turn over to St. Basil all of the chests containing the coins and jewelry which had been paid as taxes by the people of Caesarea. But now St. Basil was faced with the daunting and impossible task of returning these thousands of coins and pieces of jewelry to their rightful owners. After praying for a long time before the icons of our Master Christ and His All-Holy Mother, St. Basil had all the treasures baked into one huge pita. He then called all the townspeople to prayer at the cathedral, and, after Divine Liturgy, he blessed and cut the pita, giving a piece to each person. Miraculously, each owner received in his piece of Vasilopita his own valuables.