Going from context, she was showing them around and gets called by the director, so she tells him "I gotta go! Sorry!
However I'm stumbled on this usage of 適当にしてて. From context I guess she's just telling them.. to chill around?
適当 is a tricky word, but the meaning of 適当 in this 適当にする is "random; whatever; laid-back; without giving it much thought" rather than "appropriate". 適当にしてて means that the listener can spend time however they like since there is nothing specific to do. Since this seems to be a party, it means they can enjoy talking to someone or having a drink. If I understand correctly, "to chill around" could be a possible translation, but 適当にする doesn't strongly imply relaxation.
Me personally, I'd translate that line 「適当にしててもらっていいですか？」As "Can you cover for me?"
適当にする、literally would be "Do as appropriate."
適当にしててもらう。To have it arranged so that someone would do as appropriate.
適当にしてもらっていいですか？ May I ask you to arrange things so that they would be dealt with appropriately?
...which is basically saying, hey, I'm busy, gotta jet. Can you cover for me?
適当 here means (something) moderate (cf this question).
So it means to do something moderate, or to pass time moderately. To chill around could be a translation, but mainly the idea is captured by around. What action is implicit depends on the context.