in the larger context of the verse, this line refers to some of the places that will conjure up memories of Jay-Z's life and legacy. crime-ridden areas ("darkest blocks") and the kitchens of drug dealers represent locations of those to whom he relates
Through the darkest blocks refers to blocks that are metaphorically dark due to crime, poverty etc. Many of these blocks Jay-Z once lived in as a youth. To earn money, he would cook crack/cocaine which involves boiling cocaine in pyrex glass on the stove
Barber shops are a traditional venue for African-Americans to congregate. Oftentimes, African-American males will socialize at a local barber shop with their friends, debating current events, gossiping and telling tall tales.