"She recently went to Atlanta."
Translation:Вона недавно їздила у Атланту.
If we assume that you just want to state a fact that something happened in the past, then you use "їздити" (Вона їздила...). Just saying "Вона недавно їхала в Атланту" on itself sounds incomplete, because you stress the process of going and now you have to say why you do it (e.g., something happened on her way).
If you want to stress the fact that she has not returned from Atlanta, you would use "Вона поїхала ..."