Norwood is a beautiful neighborhood in the shadow of Montefiore Medical Center, so you might find yourself doing some of your shopping on 204th street with lunching medical students and nurses. Actually, if you get further North-West in the neighborhood, you'll see resident housing for medical students and other offices owned by the hospital - of course all impeccably maintained.
The southern edge of the nabe is Mosholu Parkway, which is really a stretch of green space connecting the NY Botanical Garden to Van Cortlandt Park. If you are into jogging or running, or just hanging out under a tree on some nice grass, the Mosholu Parkway (and Norwood) is for you.
This apartment is very reasonably priced at $875/month and the pictures seem to be nice.
The shopping stretch on 204th includes a lot of mom and pop stores, a CVS, a Foodtown, great fresh vegetable stores, a fish monger, an Albanian butcher, a diner and a few of the old bars, like McDwyer's and McMahon's, left over from Norwood's days as a stop on the Irish Immigrant railroad (when the neighborhood was called Bainbridge). There are also a few decent Latin/Mexican places, of which my favorite is Rio Mixteco down near Webster Avenue and 204th. You have to try a chorizo taco... mmmmmmm!
There is a D train stop right in the heart of Norwood on 205th Street (last stop on the D). Don't let the terminus of the line scare you though, the D runs super express in the am/pm rush. The train is over at Mosholu Parkway and Jerome and the Metro North is at the Botanical Garden.
Another great aspect of Norwood is the misnamed Williamsbridge Oval, which Boogiedowner has covered in the past. The Oval just underwent a multi-million dollar renovation. There are the obligatory hoops courts and playgrounds, but even a dog run and really well maintained tennis courts (that actually get used!). In fact, the Museum of Bronx History is housed right outside of the Oval at the Valentine-Varian House.