I think it took me a good 3 years to figure out just how accessible the garbage center was in our town.
In the beginning it seemed almost impossible to get rid of large garbage items (like broken furniture, old clothes, ect).
Thankfully, we figured out that we can cart all the random junk from our home, as well as overdue garbage and recycling bags, to the center for a very minimal fee. It's usually about 200 yen for the firs 50 kilos. Just today we carted over two broken floor chairs for 200 yen, and the apartment feels so much cleaner and roomier for it.
I definitely agree that having paper towels and some basic cleaners on hand for your successor would be helpful (along with a note on what each is used for). Something for kitchen/window surfaces and bathroom surfaces is essential. Tatami cleaner is a bonus gift.
We came to Japan and were greeted by an empty apartment...our preds had broken their contract, so we started from scratch. Even so, our apartment needed a wipe down, and then we had the job of furnishing it. The best part of furnishing an empty place is that all the stuff you get is clean and new, so in a way, it was blessing in disguise. Alternatively, I heard horror stories from our BOE ALT's who found out last minute what a disaster one of their fellow ALT's left their apartment...and all of them teamed up together and went over there the day before to clean it up for the new person.
Honestly, if you feel like cleaning your apartment is going to be a job that is too big for you to handle, be honest and get your friends together to help you do it. Many hands make light work