Emory is a bit of an island but uber can get you to a good number of fun places for less than 15 bucks (most of the time less than 10). There's a few restaurants within walking distance of the SAAC, right up at the clairmont/north Decateur intersection. There is also a publix up there.
Nightlife Areas: Atlanta has everything. Try out some different areas to see what places you like best and just cause one bar in a particular area sucks, Doesn't mean there's not another across the street that has a totally different vibe.
Highlands - about 10 min away. Tons of bars and tons of food options. Young professional crowd.
Buckhead - about 20 min away in a fast uber. Lots of bars with a bit more of a frat feel to them (lots of GATech people and UGA people go here on the weekend). There's one block that's basically got everything.
Edgewood - 15ish min away. if you're into the dancing scene, this is a good spot to go for loud music and crowds without having to hit up actual clubs. Very eclectic crowd.
East Atlanta village - bit further from you. About the same distance from buckhead. Maybe a bit further? Interesting place that's similar to Edgewood as far as crowds but less dancy (graveyard is usually bumpin though).
Mitown - 10 - 15 min away. Maybe someone else could chime in here. I don't go there a lot. There's some clubs and bars and it honestly has a bit of everything but things arent quite as bundled together as other sections of town (in my own opinion). Little more difficult to bar hop.
There are good food options EVERYWHERE. And you have a publix close by so you should be fine with groceries.
The SAAC is a nice facility. Its not an A+ facility (although the pool is great) but it's got pretty much everything you could need to work out and stay in shape. Emory is a bus hop away and has the woodpec which is a bit better but I don't know about entry without student ID. I haven't been in a few years.
If you have any questions, feel free to message me. I've lived here for 6 years and went to emory undergrad and am currently at Rollins.