Somewhere refers to a specific place while anywhere refers to, well, any place. However, it is one of the endearing (or frustrating) traits of English that those two can mean the same thing at the same time. Sometimes.In 

The Wizard of Oz, Dorothy sings of "Somewhere over the rainbow," which refers to a specific place of happiness she might someday visit. She is imagining a single location.

In the song "Anywhere I Go" the neo-ska / permanently stoned band Slightly Stoopid talks about "Anywhere I go I choose to be with you," meaning wherever "I" go, be it Kalamazoo or Djibouti, "I" will choose to be with "you". This could be any location.

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/forum.wordreference.com/threads/sometime-anytime.1966585/:

 Are you free sometime/ anytime next week?

"Anytime" is just a shorter way of saying "at any time". 

"Sometime" is a shorter version of "at some time". Both work fine in your question. You can use adverbs in questions and negative statements that aren't formed with "any":Do you sometimes have doubts? Should I call you sometime next week?You are right that "any" is generally used in negative statements about things:Do you have any/some time? No, I don't have any right now. (I couldn't use "some" idiomatically in my answer here)This pattern doesn't apply to the adverbs "sometime" and "anytime" in your question, though.

Für sometime ist das auch ganz gut:

engvid.com/vocabulary-sometimes-always/