The neighborhoods along the Kennedy between the junction and downtown - Avondale, Logan Square, Bucktown, Wicker Park, and West Town - are chock full of restaurants worth considering. My personal favorites are
Mexique in West Town for contemporary Mexican with a French accent,
Lula in Logan Square for farm-to-table cuisine,
the Bristol in Bucktown for new American gastropub cuisine,
Dos Urban Cantina in Logan Square for contemporary Mexican,
Yusho in Avondale for contemporary Asian, and, if you're dining during breakfast/brunch/lunch hours,
Jam in Logan Square.
A note about parking. These areas are popular, especially where the restaurants are located, and you'll be looking for street parking, since there aren't many garages and lots like downtown. You sometimes can find it on the side streets, other times only on the main streets where you'll need to feed the pay boxes. Depending on the day and hour, you might be driving around for a while looking for a space.
gastro and Ronnie mentioned restaurants off the Edens, while you asked about places south of the junction. If the Edens works for you too, I'd add
Wholly Frijoles in Lincolnwood, and
Libertad in Skokie.
Last edited by
nsxtasy on June 3rd, 2016, 2:23 pm, edited 3 times in total.