A tip I once read in a woman's magazine was from an elderly lady who was a widow. Every night she would say to her dead husband: "Right, Fred, I've put the cat out and locked the door" out loud. This seemed a good idea to me when I read it all those years ago as a schoolgirl, and now I'm in my dotage, I've taken to using it to tell myself I've switched off the iron, locked the car/house, etc.
As for remembering where you've put something - it's not too late to train your memory, I reckon. If putting something in the same place every time just doesn't work out for you, take a couple of seconds when you put your glasses/keys/phone down, to look at it and take a mental pictures of the surroundings. Or remember your thoughts at the time.
If you've come in and rushed to the loo, you may have left your keys on the washbasin in there, so you should remember that and can go back and find them again. If you put them down on the kitchen work surface while you unpack the shopping - stare at them for a bit before carrying on and imprint that picture on your memory until you start looking for them again....
Or you can use the "saying things out loud" trick for that, too - "Don't forget, Mary" you can tell yourself, using your own name, of course, or that of the cat, perhaps, if you feel silly talking to yourself, "Don't forget, Tiddles: I put the remote control on the table in the hall when I went to answer the door"
I suppose I do have regular places where I keep things, although I am on the wrong end of the tidiness spectrum.
I keep my mobile phone in my bra. I keep keys in my pocket, but only trouser pockets - not jacket pockets because I might be taking the jacket off. And my glasses can regularly be found on top of the dishwasher, when I have to take them off because they get steamed up when I open it!