"Inspection": visual only. technically can't touch anything, though you have to provide access to all areas. "room" is a place people travel in and out of, a closet isn't a "room". Practically every landlord is going to have inspections in their lease. They'll typically have a "how often" and "how much notice we will give you" section, sometimes with a little (or a lot) of wiggle room in the wording. Example: "Tennant acknowledges there will be monthly inspections on or about the first of the month, more often if damage was found in a prior inspection. 24 hours notice will be given prior to the inspection." That would usually be followed up with "we probably won't ACTUALLY do an inspection every month, just if we have reason to believe we need to." IE they have reserved the right and you have been notified. (I've rented several times in the past)
"Toss": Anything goes, short of physical damage of property not hindering the search - if it's locked, blocked, or otherwise secured, it can and probably will be broken into for inspection. Prisons do tosses both random and periodic, searching for contraband. Citizens that have not had some of their rights suspended are usually the ones subject to a toss. Boarding schools (with the written permission of the legal guardian) and military bunks (where you signed away most of your rights to privacy) are also tossable. That's why crypto pisses off law enforcement - usually they can sufficiently toss any location or evidence with enough force, but math can't be coerced with a bolt cutters, axe, or cutting torch.
So in summary, if you're only subject to inspection (and not a toss) then simply placing something in a closed dresser drawer is safe. There are exceptions - a dog that that has identified possible drugs can subject the specific area identified for tossing. Signs of distress also count, such as a blood trail or cries for help. Being close to an international border, using mass transit, or entering a military/government facility can also make you subject to tossing. There are other exceptions you're even less likely to need to worry about.
Geek facts: if it's displayed on your screen, they can read it. (same for papers sitting on your desk, but do not touch/move/lift!) Cops have more than once sat down at a computer (with unlocked screen saver) while doing an inspection (no warrant) and opened documents on the desktop, that's always judged to be an illegal search. This is called the "plain sight" rule. If the cops come over to talk to you about the stereo being up too loud and while you have the door open they see the bong on the coffee table (or smell the weed) that's "plain sight" and you are now subject to a toss.
