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.
Palmyra sits on the standard tourist trek around Syria and should be considered in this light. Intense competition for business amongst local outfits can make the experience some what overwhelming to the traveller who has come from the North, and has enjoyed a relatively 'quiet' trip thus far. 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.
It is worth mentioning that despite the recommendations of Lonely Planet, a day trip from Damascus could easily be enough of Palmyra for most travellers. The ruins themselves can be covered in less than 2 hours (unless you are an archeologist or particularly educated in this field of study), and if you have just come from Aleppo and the dead cities, expect more of the same in a desert setting. If you stay longer than necessary, Palmyra can be a truly depressing place and a textbook case of unsustainable tourism. To explain:
As a comparison, Siem Reap in Cambodia springs to mind, or even Agra in India. Use that as a method of gauging whether or not this place is for you. If you hated Siem Reap and Agra's artificial tourist oriented comfort, then stay away from Palmyra. A Las Vegas in the middle of Syria, whatever Palmyra used to be has been sucked up by the vacuum of greed and exploitation of local services; all that remains is a vacuous shell of culture and authenticity. The main street is clogged with touts, tourist cafes, fake souvenirs and postcard shops -- vendors roam the streets hassling you, taxi drivers are aggressive and unfair and countless package tour groups of annoying rich old Europeans wander through the streets encouraging and perpetuating this mess of a tourist attraction.
Honestly, a good itinerary (especially if you're pressing on to Deir-a-zur, or Aleppo via Homs) is to leave Damascus early in the morning, have lunch in Palmyra, spend the afternoon in the ruins, spend the sunset at the citadel, then get the hell out without handing over your money to outrageously inflated prices not seen anywhere else in the country. Sorry to be so harsh, Palmyra, but this needs to be said.
Watch out though for the "Cassanova" camel drivers--for S£200 they'll take you ladies out for a tittilating ride.
There are no ATM's (that accept international cards - there is one for Syrian cards) in Palmyra or even a full-service bank. Hotel Bel (on the main street) will do advances on both VISA and Mastercard for a 20% commission. There is a local exchange office by the museum which will change foreign currency but will not change traveller's cheques. Make sure you have sufficient cash, Syrian Pounds, US Dollars, or Euros, for your time in Palmyra.
Note that, as per usual, the Syrian Commercial Bank offers terrible rates and adds commission. You'll get a better deal by checking the rates online then changing with the shop owners in the Souq.
Souvenir shops abound on the main street with all kinds of jewelery, handicrafts and other wares typical to the Bedouin places, many of which may be nice to buy, depending on what you like. Shopkeepers (in a town with few sources of income other than tourism) are masters in the art of making you part with as much money as possible, so it would be wise to only carry as much money with you as you are willing to spend on souvenirs (and food - see below) to avoid being talked into spending all or most of the money you have for the rest of your trip in Syria. Typically souvenir shopping would happen around dinner, as many of the restaurants and shops are in the same main street and you would happen to walk past them on your way to or from the hotels and restaurants.
New Palmyra Restaurant / Pancake House on the main street for most tourists, al-Quwatli. This is a traditional Palmyra restaurant - catering for the tourist hordes. The owner is well connected with an army of scouts corralling tourists into the restaurant. For the adventurous traveller, fake ISIC student cards can be purchased for 7.50 euros, although they are of poor quality and little use in the Middle East.
On the same street are several stands selling roast chicken (half chicken for take away is 100 SP, hummous 25 SP, salad 25 SP), although you'll be lucky to get those prices.
If you venture on any of the main roads running north you will find felafel stands and other small restaurants selling the typical range of Syrian fast food bakeries selling sweet treats and plenty of convenience stores with drinks and snacks.
The only bars in Palmyra are inside the hotels, such as the Cave Bar in the basement of the Ishtar Hotel. The bar carries good selection of local beers and wines, and you can have your drink in the terrace of the hotel if you wish.
On the main tourist drag, the Hani Internet Cafe inside the Traditional Palmyra Restaurant is conveniently located but charges a pricey 50 SP for a half hour. This may be negotiable in low season. Locals can direct you to an internet cafe slightly north of the centre which only charges 20 SP an hour but has irregular hours.
Buses depart frequently for Damascus, Homs, and Deir-az-Zur.The bus station is a little under a kilometre away from the main street, so do not pay anymore than 50 Syrian Pounds for a taxi with your luggage. For other destinations, you may need a private car.
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. Private tours are the real money maker in the Syrian tourism industry, so expect to pay as much as S5000 (US$100), if you're heading for Aleppo or Hama. A bit less to Raqqa.