Normally, I recommend storing everything you own in containers out of sight, but even I can acknowledge that that has some limits. First, tucking everything away may not align with your unique cleaning style. Second, life is just more complicated than that; you probably have miscellaneous items that you struggle to store within those guidelines. That's why you need a tray of some kind in every room to catch the little things that don't quite fit anywhere else or are too frequently used to justify putting away.
The rules of the catch-all tray
When I say catch-all tray, I mean something a little decorative that can rest on a flat space in any room, holding the high-touch or random items you pick up and drop. The easiest example here is a little tray by the door to hold your keys and your AirPods when you get home, but you can have a larger tray in the kitchen to hold mail you need to sort or respond to, one in the living room to hold cables or remotes, one in the bathroom for jewelry you take off to wash your hands or put on every morning, and one by the nightstand for your sleeping mask, retainer, etc. Consider having one that's designated just for junk and miscellany, the things you know you need to put away for real at some point but just don't have time for. One of those in each room can be crucial. A major component of many cleaning and decluttering techniques is working in small spaces and categorizing your items as you go. You don't want to be cleaning the living room and taking each individual item out into a separate room to put away, one at a time; clearly, it's better to gather all the kitchen or bathroom items that are in the living room, then take them to their proper place all at once. A catch-all tray helps you do that over time, eliminating the need to go around the room looking for what's out of place. It's all there in the tray.
With that in mind, here are some general rules to consider before adopting the tray system:
Keep it on the smaller side so you're regularly filling it up, being reminded you have to actually empty it out and put everything away. If it's too big, it will just become a junk holder and cleaning it will be overwhelming.
Set a schedule to regularly clean it out and put everything where it really belongs. This doesn't have to be a hard and fast rule. You don't have to set an alert in your phone for a certain time every week (though you definitely can). Still, generally try to remember to organize the tray weekly or so, sticking to a day or time that makes sense.
Catch-all tray ideas
To be effective at catching everything, the trays need to be accessible, which means they need to be out where you can easily reach them. For that reason, they should look nice. For typical storage, I recommend a lot of plastic bins and industrial-looking containers, but for this, that won't work as well. You don't want an ugly plastic box on your side table. Luckily, there are pretty ones out there in a variety of styles, colors, and themes, so you can find one that matches the vibe of any room.
Something like this rattan serving tray, with slightly raised edges, is pleasant enough to look at while being functional for things like papers and larger items.
A slightly larger bowl or dish in a major room like the dining or living room could also be a big help, especially for items the kids bring around the house or things you use in multiple rooms. Look for something like this:
You also want smaller ones for little spots all over your home. Search "ring dish" or "decorative dish" and you'll get some lovely options like this: