I recently discovered a nice resource. It is OpenJurist.org. It is not directly related to the American Presidency but it does have tons of free access to many Federal Court Cases some of which have involved Presidents.
The site describes itself, "OpenJurist's mission is to provide access to published court opinions without charge. We currently have over 600,000 opinions from the United States Supreme Court and United States Courts of Appeals from the First, Second and Third series of The Federal Reports."
As a librarian, I have access to Lexis-Nexis which has all of the Federal and State cases. However, if you don't have free access to that resource, this is a good alternative for many Federal cases.