The first questions you should be asking is about grandma's arthritis and her hand strength. At 80 years of age, I'd be surprised if she doesn't have some form of arthritis in her hands. That will help determine some form of semi-auto is indicated or if a DA revolver will work for her.
Another factor is how clear her mind is to learning new things. Unfortunately we've seen many seniors who have a hard time remembering what they've just learned unless they go through several days of repeated drills with a monthly refresher. This is familiar to those working with many seniors.
If she cannot work a DA trigger, another option might be to find her one of these;
Beretta Model 86 Cheetah .380 ACP
These single-stack "tip-up" barrel .380's offer enough power in a larger than normal frame for a pocket gun. The tip-up barrel eases loading and unloading, making slide manipulation unnecessary. The extra size and weight makes them a fairly nice shooter as well.
In the recoil department, a .38 special with wadcutters or standard pressure LSWC loads at around 770 fps will work fine. But there are still other alternatives.
S&W Model 31's - 2 & 3-inch barrels, .32 S&W Long Ctg.
The S&W Model 30 or 31 in .32 S&W Long are not huge fightstoppers, but they offer six shots in a J-Frame package. Their low recoil allows Grandma easy control when firing. And if she's pointing at someone it's doubtful they'll do anything but assume it's a .38 or .357 in her hand. At close range the .32 S&W Long can easily be lethal.
A step up in power is the .32 H&R Magnum. While it has a much louder bark, recoil is surprisingly light. Ruger, S&W and Taurus make six-shooters for this caliber. The revolvers chambered for it will also fire the .32 S&W Long.
S&W Model 432PD (The 431PD has an exposed hammer)
The .32H&R's were slow sellers, so you may be able to find one inexpensively.
Whatever she decides on, give her your support and help in learning to safely handle her gun and to shoot it well.