If Skokie is too far east, Andersonville is probably even less convenient for you, but just for completeness, comments on a few North Side delis (and one or two downtown) are available in
this thread. I've been to J.B.'s recently and little has changed, although the candy selection is much, much larger than it used to be. (And my assumption about the deli case and bagels was wrong; both are still present.)
On the off chance this ends up being your destination, M. Henry, a couple of blocks north of J.B.'s, and A Taste of Heaven and Swedish Bakery a few blocks south, all sell baked goods worth the consideration. (M. Henry's vanilla cupcake just might redeem every bad yellow cake I've ever eaten, I could be coaxed to say. It's made me believe in the genre again.)