haha...I think I use a combination of the two that you mention.
I usually try to remember where the item might be...sometimes this involves the 'why' and what else happened on that date...sometimes even referencing the calendar or check book to see what date we went to town, etc as that sometimes relates to the 'lost' item.
BUT, I'm neat and methodical when I'm looking and very thorough so that I can say for certain that the lost item is not in those places I've looked.
My guy looks but does not always 'see' so usually I will look in those places also.
And then, one of the fortunate things as we get older is that we often just forget what it was we were looking for and that tends to thin out the important missing things from the inconsequential
"We're all just walking each other home." -Ram Dass
"Be a lamp, or a lifeboat, or a ladder."-Rumi
"It's all one song!" -Neil Young