Palmyra is in Syria.
Palmyra (the roman name) is known as Tadmor to the Syrians. Both mean the same thing - date palm. The name comes from the lush oasis adjacent to the city which is home to some million date palms. It is the only oasis in Syria.
The major tourist attraction of the area is the stunning ruins - the most famous and well-preserved of which are the Temple of Bel, the colonnade, the funerary towers, the hypogeum of 3 brothers, and the Arab castle. All are within a few kilometers of each other.
There are no ATMs in Palmyra, and the local exchange office will not change traveller's cheques. Make sure you have sufficient cash for your time in Palmyra.