I teach up in the Bronx and can recommend two very good places if you want to take a quick trip and try at least one dish that I know for a fact is unavailable below Washington Heights....
1) Take the 4 train to Burnside. Get out on the left hand (facing north) side of the tracks. There is a tiny restaurant right there on Jerome. Go in and ask for mangu (mahn-GOO), which are mashed plantains with stewed red onions. Phenomenally delicious and unavailable in most of Manhattan! The roasted chicken is also amazing, the perfect mix of crispy and tender.
2) Then, walk (or take the 30 bus) up Jerome Ave to the Kingsbridge 4 stop (it is currently closed). On the right-hand side of the street is a Vietnamese grocery store called Hung Phung. Go in and order anything, it will be delicious. Hung Phung is also quite unusual as it is probably the only Vietnamese place for blocks around. I am partial to the beef soup, it's some of the best I've ever had and very freshly made.
Happy eating and be sure to post your experiences here, good or bad! These are 5-8 dollar meals, so go with that in mind.