Oh, there are several exits, that is why there are several escalators of varying lengths.
A little hard to give directions since I do not know where you will be sitting on the train, etc.
But basically, when the train stops at Peachtree Center you want to follow the signs or ask people for Peachtree Center itself. Which will be upstairs and to the train's right. (as the train stopped, northbound, from the airport)
Note that Peachtree Center is a large complex of offices, hotels(but not yours, not directly), food court, etc all out of the weather. connecting walkways, etc.
You need to go to the train's right(as you arrived from the airport).at the right and upstairs, You will walk through the faregate, turn right and then turn left and ride that escalator. (it is one of the longer ones)
At the top of the escalator,make a sharp right turn and you will see revolving doors. Go into that, to your left, --that gets you instantly in the Peachtree Center Food Court.
Then just keep walking straight---as straight and long as you possibly can. You will pass through the food court and find yourself on a catwalk over the streets and over a parking lot. Down near the end of that is the Hilton Hotel.