I don't mean to sound pessimistic, but I don't know if the term "hot neighborhood" hasn't gone the way of the dinosaur. I believe that the new mortgage guidelines will prohibit any neighborhood from extreme levels of appreciation. Hot neighborhoods were created with the "cloud a mirror, get a mortgage" guidelines that led to an over funded, over heated marketplace. Those days are thankfully over, although as in physics, every action has an equal reaction, and so we are stagnating in a morass of over restricted lender requirements.
But I digress. . . Look at West Town, particularly those areas between Kinzie and Chicago Aves, west of Western (Smith Park a.k.a The Patch) and just west of Western Ave between Chicago and Division and North to Fullerton. Edgewater Glen, Magnolia Glen are also noteworthy if you want to be close to the lake. I still think Albany Park and especially Avondale is affordable.
Good luck in your search!