The correct revision is: Remove the comma after “apples” and put a comma after “upstate.”
The revised sentence would read: "We picked these apples when we went upstate, which was on Tuesday."
In this revision, the comma after "apples" is unnecessary because the clause "when we went upstate" is essential to the meaning of the sentence, while the clause "which was on Tuesday" is a non-restrictive clause and requires a comma.