Downtown Love refers to people who are never in relationships for long because they are always looking for something new, and/or always craving more attention.
Girl, you left him after a few weeks and now you're after me? I don't want none of your downtown love.
Any of a variety of weekly free magazines/newspapers circulated in large urban centres with a primary focus on the music and arts scenes. Some may expand content into politics, various activism, and world affairs.
Heypick-up a downtown rag and check the shows this week.