First recorded by Chuck Jackson (1962, released 1984).
First released by Tommy Hunt (1962).
Hit versions by Dusty Springfield (UK #3/IRE #5/AUS #16/NETH #5 1964), Dionne Warwick (US #26/R&B #20/CAN #26 1966), White Stripes (ALT #25/UK #13/AUS #54/NZ #34 2003).
From the wiki: “‘I Just Don’t Know What to Do with Myself’ was written by Burt Bacharach and Hal David, and was first recorded by by Chuck Jackson (‘Any Day Now‘) in 1962 in a session produced by Jerry Leiber and Mike Stoller, with Burt Bacharach arranging and conducting.
“Jackson’s version was shelved and remained unreleased until it appeared on a 1984 compilation titled Mr. Emotion. The same backing track and Bacharach arrangement was then used later the same year when Tommy Hunt (‘Any Day Now‘) covered the song. Hunt’s version was released as single in May 1962, but it did not chart.