I like Claudia's ideas, especially about making an occasion out of a black cab ride.
I just saw an item that can add to that experience – it's about the little green sheds. You could get breakfast at one to round it all out.
Thinking about more active, outdoor kind of things, here are some suggestions.
Hampton Court Palace for sure. It's more interactive than the other two, has lots to explore indoors and out, and you're still in Oyster Card territory, not travelling very far.
Greenwich, whether by DLR or by boat, is another cool experience, with the option of walking through the tunnel under the River Thames, and also walking to the top of the hill to see the fantastic view and the Observatory. Even if you don't go into the Observatory, you can stand on the Prime Meridian. (There's more to see at Greenwich, I'm just tacking on a few things your grandson might enjoy as part of the mix.)
Camden Market isn't my favourite place (I don't like really busy places that much) but it's a spectacle just riding the bus up the street. Of course lots of people love the market, I'm not saying don't go in. I like walking around the lock and alongside the canal. Canal boats will probably be a new thing to see, and there's almost always one going through the lock.
At Covent Garden there is an ice cream place I like (Venchi) because the ice cream is tasty and you can look down at the musicians on the lower level while enjoying their performance. Outside the Punch and Judy there are often performers entertaining the crowd for donations.
The view from the top of the tower at the Tate Modern is quite something (new and free).
Edited to add: I am not a sports fan but if your grandson is, maybe you can go to a match of whatever's playing when you're there.
If you can contrive to see cricket, even just on a green, that is probably going to be new. On Sundays you can get a lovely roast lunch at a pub and then with luck see the locals in their white outfits out on the cricket pitch.
It's so wonderful that you're taking him. Lucky lad to have such nice grandparents.