Recommendations on a pistol for my grandma.

To expand a bit on what Twigg said:

She absolutely must pick out her own gun. We can suggest options you might not have thought about, but ultimately it's her gun.

Size is a real big issue for a concealed-carry gun, but not so much for a nightstand gun. Comfort and controllability become far more important. Part of controllability is the ability to operate the gun easily, not just control its recoil.

And on that subject, there are a few reasons to not get a .380; power is one, but relative recoil also counts. It seems counter-intuitive, but the .380 pistols frequently have recoil that is sharper than 9x19 (9mm Luger) pistols, even though they are significantly less powerful. The locked breech design of the 9x19s helps damp the recoil.

Although I'm a dyed-in-the-wool 1911 fan, I do not recommend them to most people. I'll just sit next to Twigg in the back of the room and join him yapping about wheelguns: a double-action revolver is one of the most simple, useful tools ever invented by mankind. Small-framed women of my acquaintance have universally fallen in love with a 3 inch barrelled J-frame sized .38 Special.

Ahh, quite true, but the reason they are locked breech is that they are tiny and light. The designers went to locked breech specifically so that the guns could be made smaller and lighter. Small and light makes for increased recoil, regardless of the locking system.
A straight blowback Bersa .380 has far less felt recoil than a Ruger LCP locked breech .380, because the LCP is tiny and weighs almost nothing.

And we'll just have to disagree on the recoil issue of a snub .38 v. an LCP. Sure, you can make a snub recoil a lot more, but not until you make the ammo more powerful than a .380 ACP. At similar ballistics, the revolver's felt recoil is the same or less.
However, I know you'll agree with me that the revolver has the distinct advantage of being able to reliably shoot everything from light wadcutter training loads to full-house defensive ammo, whereas an auto has a much more limited range of useable ammo.

Eurocops in the '30s and '40s carried .380, so that makes it a good choice today? C'mon woodstock, that's a specious argument and you know it. Shall I counter with the NKVD's use of the Nagant revolver in 7.62x38R? Eurocops carried .32 ACP at least as often as .380 ACP, and U.S. police of that era frequently carried various .32 revolvers, but you aren't suggesting .32 ACP or .32 S&W (or 7.62 Nagant) are good choices for a bedside gun, are you?

Don't get me wrong, I own an LCP and a P3AT and a Smith 640 Airweight, and pocket carry all of them (interchangeably, not all at once ). But none of them are bedside guns, and that's the topic here.