Clairmont Campus...
The good thing is convenience. Walking distance to campus, many shuttles to campus if you don't want to walk. There are also shuttles to Publix on weekday and Kroger on weekend (people without a car can survive!).The only bad thing I can think of is the rent is a little bit high(700 to share a kitchen and living room with one roommate).
Yan

Off Clairmont Road...
Living just off campus means that you can walk or bike to school everyday without having to drive. It means that you enjoy almost all the facilities that bring living on campus without actually living on it. You have the feeling that you are not always in the University without actually having to go that far from it.
Omar

Off Clairmont Road...
The advantage of living off campus is being able to wake up ten minutes before class and it not being annoying to go to lab for a couple of minutes to set up cultures for the next day. Also being able to walk or take the shuttle means that you don't have to worry about a car or about getting to school when the car is in the shop. It makes the hours that you put in as a grad student not feel so bad because you lose no time in the commute.
Ellie

Decatur...
It can be a little pricey to live here, but it's a greener (i.e., more vegetation) part of the city and not too rowdy. If you're looking for more diversity and nightlife, you'll have to travel elsewhere though.
Sean and Neil

Lilburn...
There are really great public schools out in the 'burbs so it is a good place to raise a family. Also if you are buying a house you get much more for your money in the suburbs. The commute is okay--it takes me about 30 minutes to get to school from where I live. I do miss the city sometimes; there is so much going on in the city that it can feel a little isolating to be in the suburbs, but it is just a short drive, so that feeling usually passes!
Karyn

Midtown...
Restaurants, MARTA, Piedmont Park, independent movies, Trader Joes, Atlanta Botanical Gardens, all within walking distance. Who could ask for more? But the downside is the tremendous amount of car and foot traffic all through midtown.
Karoun and Lynn

Emory Housing links
On campus- http://www.emory.edu/HOUSING
Off campus-http://www.housing.emory.edu/off-campus/home.cfm

Note
Emory is in the city of Atlanta, in Dekalb County. Many apartments will list themselves as "Emory area". Other convenient locations: Decatur (1-5 min.), Toco Hills (5 min.), Little Five Points (5 min.), Virginia Highlands (5 min.), Midtown (8 min.), Buckhead (10 min.), Avondale (10 min.) and Stone Mountain (20-30 min.).