@LyssaKi
Was the sim's home lot dirty when you left?
I'm not absolutely sure yet, but it appears to be that the cleanliness state of your home lot follows you to other places. Look at the buffs on your sim to see if they still have a cleanliness buff of some sort when you get to where you travel to. If your home lot is dirty, then wherever you go will get dirty if you stay there long enough. If your home is pristine, then wherever you go will also be that way. I'm still testing this though so right now it's more of an educated guess.
So try getting your home lot clean before you travel and you shouldn't see dust and dust bunnies where you traveled to.
Hope this helps.