Where are you located? Availability may depend on where you are... Kobo Touch is $99 and is wireless (allows Internet browsing) and has a couple of games in the "extras" like chess, sudoko. You will not be able to play "games" in the sense that kids want to, on an eReader. For your grandmother however, the Touch will allow font adjustments to make the text pretty much as big as you need to.
Perhaps you should shop around for a second-hand or refurbished Kobo Vox's 7" tablet which is 8 gb, expandable with a micro SD card, runs on Android "Gingerbread", has access to the Google Play Store and can have lots of apps added to it. I've heard of persons picking them up new for under $150. It's now a discontinued model about to be replaced by a new Kobo tablet (the Arc) so chances are it's price will drop before Christmas if you can wait.