Pilsen, Humboldt Park & Logan Square are obvious choices. As a Logan Square resident, I can tell you that there's something new on Milwaukee every week. Also, even the most Lincoln Parkers will tell you that the best restaurants in the city can be found in Logan Square.
In no particular order, here are my "sleeper" hoods.
1. Portage Park: Take a look at all the development going on at Six Corners. Portage Park has a very passionate neighborhood association hell bent on reviving Six Corners. New restaurants, craft breweries, etc.
2. Old Irving Park: The best hidden gem in the city. Close to 90/94 and the CTA Blue Line. Developers are salivating over lots here and I can't believe so many people have no idea this neighborhood exists.
3. Avondale: The Belmont Blue Line saw the highest ridership increase of any CTA line YoY in 2013. Purely a Logan Square overflow play.
4. East Garfield Park: A much longer term play. Close proximity to the Loop with Blue & Green line trains right there. Gentrification will continue to creep west of the United Center.