I use my starbucks card ...(with no free drink earnings ... this might be different in DTD ... not sure). I load it in Canada to get my credit card points and then use it (or my app) at locations in Disney.
The DTD locations are run by Starbucks and you can use rewards at them. The parks ones are run by Disney and don't take rewards however you can still earn stars for them. according to this site they take rewards at the DTD location on the west side http://www.starbucks.com/store/1008...0-e-buena-vista-dr-downtown-disney-lake-buena
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