In my 30-some years of life, I have moved a lot. Like, really a lot. Since I graduated from college, I've probably averaged a move every single year. That's a lot of boxes and bins, a lot of heavy lifting, and a lot of new kitchens.
I've gotten pretty good at it and, in a weird way, I almost look forward to moving: It's a time to get rid of those things you never, ever use (rule of thumb: If I haven't used it since I last moved, it's time to let it go) and a time to clean the things that you should really clean more often.
Admittedly, my penchant for cleaning and organizing things is not normal. You might not look forward to cleaning your KitchenAid stand mixer with a toothbrush or making your faux-granite countertops sparkle *almost* like they're the real thing, but there's one thing you really should do.
The one thing you should really do — and I'd argue it's the first thing you should do before putting anything away or even thinking about where your slow cooker should go — is pull out your refrigerator and clean behind it.
Warning: There may be some really gross stuff back there. During my most recent move, I discovered big gray clumps of dust, cereal, a nail, and some pieces of plastic. Two moves ago, it was so filthy, I can't even talk about it. I'm pretty sure there were mouse droppings.
Just so you know, these were not particularly dirty apartments; actually, they were cleaner than most, which is why I think it's so important to move your fridge. Even people who clean regularly don't think to clean behind their fridge.
I recommend a three-pronged approach to cleaning this area: First, I sweep the floor behind the refrigerator and underneath where it usually sits. You may also need to vacuum or mop or both, depending on how dirty it is. Second, I use a handheld vacuum to suction any dust that's in the fridge's vents. Finally, I like to give the sides and the top of the fridge a good wipe-down. (It's also not a bad idea to give the inside of the fridge a good cleaning before you hit the grocery store!)
Then I'm ready to move it back in its place and start getting settled.
A caveat: Obviously, if you have a built-in fridge, this is not possible. In my rental kitchen experience, however, I have only had free-standing fridges that are pretty easy to move.
What's the first thing you do in a new rental kitchen?