smithym said:
You may find it hard to find any major airport that will let you store luggage over night due to security risk. You would have better chance at leaving it at a hotel where your staying. I have done this a few times at hotels near LHR with no dramas.
LHR has a left luggage store. I used it in June. Also used one in HKG around the same time. All luggage going into the store is x-rayed, so I don't see why it would be a (significant) security risk.
Googling "xx_ left luggage" (where xx_ is the IATA airport code) showed links for SYD, BKK, LAX and JFK. I stopped there because they seemed a reasonable selection of "major airports" to me.