I've lived in Woodlawn for nearly two years. It's a close-knit Irish neighborhood with a true "suburbs in the city" feeling. Wonderful pubs and bakeries on Katonah (main drag) and McLean Ave (in nearby Yonkers). Though you'll find basic amenities (grocery, laundromat, etc.) within easy walking distance, you'll find yourself heading to Westchester or Manhattan for major shopping, movies, the gym, or a better hospital than Montefiore's scary Wakefield campus. Since subway access is limited (bus to the 4, long walk to the 2/5 trains, depending on your location), most Woodlawn residents rely on Metro North for access to the city.
There are times I wish the area was less isolated and had more amenities, but you can't beat the cheap rent, peace and quiet, and--for students-- proximity to Fordham's Rose Hill campus, as well as The New York Botanical Garden. If you have a car, the College of Mount Saint Vincent and Wave Hill, both in Riverdale, are only 15-20 minutes away. History buffs will appreciate Woodlawn Cemetery, where Herman Melville and Miles Davis, among other prominent figures, are buried.
If you work in Manhattan and want to escape the grind at an affordable price, definitely explore this hidden gem in the Bronx!