Each ATM, the machine, belongs to one or more networks. Those networks work with multiple types of cards. Each card belongs to one or more networks. The overlap of the networks the machine belongs to, and the card belongs to determines if the card works and what fees and limits apply.
In general if the credit card belongs to one of the major networks (VISA, Master Card, American Express and Discover) you shouldn't have a problem finding a ATM that will give you a cash advance, or even a cash advance without an ATM Fee. Each credit card network should have a web interface to show you where the ATMs are that will work with the card. If it is a store credit card it still might belong to one of the major networks. If the bank that issues the card is local you can probably get a cash advance at the bank branch. Use the website to see if the ATM/Branch locations are convenient for you.
The actual limits are a function of the card type, and the credit limit that you have been approved for. In my experience the maximum amount of cash advance outstanding is half the credit limit, but you need to check with your card.
Keep in mind unless you have a special offer from the credit card company expect that there will be a fee charged by the credit card company for the cash advance, this is in addition to a fee charged by the ATM. Also remember that interest starts to accumulate on day one of the cash advance. It isn't like a regular purchase that might not be charged interest until the cycle closes and the payment is due. The documentation from the credit card company will describe all the fees and limits.