It sounds like you'll be taking your luggage with you to the interview site rather than returning to the hotel before going to the airport after your interview is over. You want to look as professional as possible, given the norms in your field and for your position. If your backpack looks casual, you might want to consider trying to use a computer bag instead. You could also take the suit separately on a hanger (wire ones aren't great, but could be disposed of at the hotel), in a heavy plastic bag like stores and dry cleaners use (but not the thin transparent dry cleaning bags) and plan (check in advance that it fits) to put your travel clothes and any toiletries into the computer bag for the return trip so that you just have one piece to take to the interview.