你可不可以去- Can you go (or not) or "你想不想去 Do you want to go ( or not) 你要不要去 (Will you go or not)

Go (去) is missing, should be included 你想不想去﹖ Do you want to go ?

you can use"你想不想去“，however,if we say,we would ask"你要不要去”，when you say "你可不可以“which means whether you have time (which is usually deceided by the condition) to go there~

Use 你想不想

I think you can use both of these two phrases in that situation. However, as native speaker, personally I think the "可不可以" might expresses more about a matter of the factor that whether he's in position to go(or capable to go/ allowed to go) somewhere. And the "想不想" relatively sounds more about that whether subjectively he want to go somewhere or not.