E. 201st Street and Decatur Avenue, 1 Bedroom - $700/month
Anyone familiar with the hood will notice this new-ish construction that a developer was trying to sell about a year or two ago. It appears that the units have gone unsold and have been on the rental market for a while.
The building itself is not the worst Fedders monstrosity I've ever seen (it's not even the worst in the hood). There are cute little balconies/terraces for everyone but the ground floor. The makeup of the building seems decent enough - not overly rowdy. There's a Mexican family, who use indoor seating as outdoor seating, a hipster with a small dog, a grand dame Puerto Rican woman who decorates her balcony with plastic ivy vines and lights.
The hood has some pretty cool stuff to offer. You'd be near the Mosholu Parkway, which serves as a long green park (with a road) that connects Bronx Park to Van Cortlandt Park. You'd be near the Bronx Greenway and great biking. The Botanical Garden is pretty damned cool as well, and until October there is a twice weekly farmer's market at the Garden.
There is decent shopping on Bedford Park Boulevard, a bit more on 204th Street across Mosholu Parkway, and yet even more down on Fordham Road. If you want really fresh and quality products like bread, cheeses, meat, fish, pasta, or produce, I'd take the 15-20 minute walk to Arthur Avenue or ride my bike over.
Fordham University and Lehman College always provide cultural offerings to the hood like lectures, talks, plays, and musical performances. Fordham provides pretty decent college sports to the nabe.
The hood is saturated in transportation with the B/D at Bedford Park Boulevard and the Concourse, and the 4 train at Bedford Park Boulevard and Jerome Avenue. The Botanical Garden also has a Metro North stop.
Further Reading for the Studious Types:
New York Times "Living In - Bedford Park"
The Real Deal "Bronx's Bedford Park Hidden in Plain View"
AMNY "Bedford Park, Bronx"