A locked trunk in a linen closet at your nearest and dearest relatives house is your best bet.

The real problem is with trying to store your stuff without owning a safe spot for it.
About as close you will get to safe storage, outside of on your own or a friend's land, might be one of those warehouse storage units.
Bus lockers and gym lockers are likely to be locked down along with the station if there is an emergency and they are pretty limited in size anyhow.
In addition to that almost all public transit locker units require you to be there daily and units that are not opened and closed everyday usually get opened by the transit company's security team and disposed of as abandoned property.

Safety deposit boxes are almost certain to be locked down if there is an emergency.