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 and perhaps the only truly tourist town.
In 2006, tourism was flagging and the hotels and tour guides were responding by raising prices and harassing anybody who looked like a tourist.
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.
DO check your camera batteries and digital chips at the photo shops located on the main street next to the Pancake House and accross from the Tower Hotel ($15/night off season/clean/great people. It's a pain to get all the way out to the ruins and find your batteries dead or your chip full.
Watch out though for the "cassonova" camel drivers--for 200 SR they'll take you ladies out for a tittilating ride.
There are no ATMs in Palmyra, and the local exchange office will not change traveller's cheques. Make sure you have sufficient cash - Syrian Pounds, US Dollars, or Euros - for your time in Palmyra.
New Palmyra Restaurant / Pancake House, a traditional Palmyra restaurant is a real treat, located on the main street in the tourist part of town. The extensive menu of local foods are very flavourful, and the pancakes would be desireable anywhere, let alone after eating nothing but Arab breakfasts for a few days.
Just across the street from the Tower Httel in beautiful "downtown" Palmyra, they also have great milk shakes and are planning to put waffles on their menu as soon as the grill is hot. Gina and her husband Iyad Ibrahim are the owners; she is from Romania so you get a good choice of Eastern European food,too. They do not take commissions from any hotels so their prices are great.
If hiring a private car, you might want to consider side trips to Qasr al-Heir ash-Sharki - a partially excavated Ummayad palace quite literally in the middle of nowhere - and Rasafa, originally a Roman city with heavy Byzantine influence, also used by the Ummayads before being destroyed in the Abbasid era. Rasafa is also of interest for the stone it's built out of, more a quartz-like crystal instead of the usual granite or sandstone. Makes for a unique appearance. This route takes you quite close to the Euphrates, and you can be dropped off in Raqqa, Aleppo, or Hama. Car hire can be price, and the driver still has to get back to Palmyra. Expect to pay as much as S£5000 (US$100), if you're heading for Aleppo or Hama. A bit less to Raqa.