Would love to see him at City as Yaya's long term replacement. I think he could play that number 10 role ahead of, for now Fernando and Fernandinho... potentially Pogba could replace Fernandinho, though that's a bit Football Manager and not sure how realistic it is. He reminds me so much of Gascoigne - always moving, always looking for the ball and similarly to Lampard, always knows who is around him and where his teammates are. The difference is that Barkley has the pace and strength to invite opposition players to try and make the tackle before using his skill to get past them and his strength and pace to push forward.
As many have said, he is by far the shining light for the future of English football, and whilst he hasn't proven himself consistently unlike Sterling has - I think Barkley could dominate and influence a game more easily than Sterling could.