A cautionary note that URLs and DOIs may not be needed for a respective reference type so best to refer to the style manual to confirm whether to include or exclude the information.
In the EndNote manual there’s usually a “Reference Type” layout of all the reference types and their corresponding fields which serves as a quick and handy reference but curiously this information seems to be omitted from the X5 pdf manual. You can instead download a copy of the EndNote X4 pdf manual* which contains the list of reference types from the “Guides and Information” section (“Help Documentation”) of the Thomson Reuter’s EndNote website: http://www.endnote.com/support/ensupport.asp
Also, if you check the APA 6th’s output style and look at the “Journal Article” bibliography template you’ll see how DOI is used. The DOi field is “linked” with the word ‘Doi’ (the single appostrophe informs EndNote to display the word). The use of the “Link Adjacent Text” creates a relationship between the two such that the word (Doi) will not be displayed unless there is information in the DOI field within the reference type itself. (Even if the word Doi was omitted from the template, the DOI field information will not be displayed if the field itself in the reference type is blank/empty.)
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*Information concerning the music and data templates (which is new to X5) will not be available in the X4 manual.