By far the most popular location for a strap button is in the treble side heel of the neck, down where the player doesn't see it, in what Richard Hoover calls the "passenger side" of the neck. Here, the strap draws perpendicular to the button and it's very secure indeed.
When I screw a button in this location, I use a thin leather washer underneath to cushion it against the finish. We don't want to blister or chip the finish. For instruments made with a conventional dovetail joint, the location of the button doesn't matter much except for the visual appeal.
Taylor guitars have bolted necks and the company provides a measurement so the strap button screw won't hit a bolt or crack the heel:
Very thoughtful and typical of Taylor, who likes to nail down all the details.
Other makers bolt their necks, and sometimes it's easy to see inside the body where the bolts come through the neck block. If I'm unsure of the bolt location, I'll get out my super-strong rare earth magnet and stick it right on the heel. It's a snap to locate the bolts this way:
Now I can drill a pilot hole midway between the two bolts for my strap button screw.
Jazz guitars and others with flat heels make the choice pretty obvious:
You can place the strap button in the bass side of the guitar next to the neck, screwing through the side and into the thick neck block.
You really don't want to miss that block! A thin guitar side is not able to support a strap button under load.
Just like drilling into a plaster wall, you want to hit a stud. It's easy to find the neck block by tapping gently on the side. The tone difference is striking when you tap over the solid block:
Some guitars, such as Taylor and Santa Cruz, have such narrow neck blocks that it's nearly impossible to place a strap button there.
What if you want a strap button in the side and can't hit (or you drill and miss) the neck block. Just glue a 1/4" thick wood reinforcement block inside to hold the screw and all will be fine. Make the block large enough, say an inch wide by two inches high to carry the load. Taper the edges nicely and it'll pass inspection if someone looks way up inside there.
I've noticed that some of the Montana-made Gibson flat top guitars have that sort of reinforcement already built in. Nice idea.
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