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.
