Actually (at least in the PC version) you can safely stash items in:
- Detroit (streets) - available from the very beginning; it's best to stash items somewhere near one of the weapon dealers, so that you can easily manage surplus stuff; a good choice would be the "Hobo corner" near gas station, not far from Sarif HQ. Also, slight story spoiler,
don't place the items in Sarif HQ nor DPD - that areas will get off-limits for/at some time.
- Hengsha (streets) - IMO the best bet is the Hengsha Whore Hotel, available from the very start of first visit in Hengsha; I think that only storing some spares makes sense here, as Detroit is visited more times and covers more of the gameplay. Also, slight story spoiler,
don't place the items in Alice Garden Pods - that area will get off-limits for/at some time.
To sum up: your apartment is not a very good place, as it's hard to use it as an effective stash - you won't be visiting it too often compared to streets. Simply use the streets; no NPC will bother with your items at all, and they will stay there until the riots start.
After that, you're up to your arm augs to help you manage your stuff, as you won't be getting back to Detroit after that, and your following visit in Hengsha will also be the last.
Note that some subareas do get reset with time (doors re-closed, barrel/boxes/computer terminals reset etc), but the loot doesn't.
Source: my recent gameplay;
all the items left in various places during the very first visit were still there during the riots.