No, we don’t say “pay there a visit.” We might possibly say “pay a visit there,” but we’d usually just say “I’ll pay a visit,” with the destination understood. As a general rule in English, there is no requirement to mention the indirect object (or include prepositional phrases) that don’t provide new information.
Also: We don't write "wanna" -- it's just how we pronounce "want to" or "want a."