So I stayed up in Washington Heights for 2 months to do a rotation at Columbia, and I didn't mind the neighborhood, but then again, I probably liked it more than most. As y'all said, it's definitely cheaper than much of Manhattan. Also, it's well connected to downtown via the A-C and 1 trains, so going down for a nice dinner/happy hour are definitely reasonable things to do (which I did every day for 2 months straight). The problem comes in when you want to stay out late - past 10pm, the express train stops running, making the return trip considerably longer... and on the weekends - fogetaboutit - sometimes it would take me ~2hrs to get home. You can, of course, take cabs, but a cab back to Washington Heights can be expensive (although I guess you can pay with all that rent money you saved), and it's not always easy to find a cab that's willing to make the journey.
As far as the neighborhood itself: So it's probably the most homogenous neighborhood that I saw in all of Manhattan - it's very Dominican, and Spanish is the primary language. I love Caribbean food, and at first I was really excited, but I quickly got tired of the lack of diversity (I ate so many plantains that I had to take Kayexalate). Also, at night, it's pretty dead - there's just not that much to do. Physically, there are parts that are ugly and dreary (the hospital is one of the main offenders), but there are also parts that are beautiful with great art deco architecture, particularly as you move north towards Inwood. 181 st (10 blocks north of the hospital) serves as the main drag for a more affluent, diverse, a very pretty part of the neighborhood - looks like a great place to live, but once again no night life, and even further away from downtown.
So where would I live, you ask? I'd take the Upper West Side, or Morningside Hts. - Both neighborhoods are more diverse, have more bars within walking distance, greater variety of restaurants, and are more accessible to the rest of city. The commute from these neighborhoods are short, because during the day, when you'll be going to/returning from the hospital, the trains run frequently and with express service. Yeah, you'll pay more and probably need a roommate, but as long as your moving to Manhattan, you might as well be where the action is... ok, my long winded 2 cents - hope that helps.