The real subtext of "Twenty Things" was "Twenty things to do by programming a computer." After all, in practice one of the most beloved things my high school students did with our computer was use its text editor to write their English papers, so when their teacher made them correct the errors in it, the task wasn't torture as it was before computers. But that isn't in "Twenty Things."
So, many of the things they list can be done all the better today without programming, and therefore wouldn't be in today's list. Making music in Garage Band is way cooler than programming Jeanne Bamberger's music box in Logo.
But there are surprising exceptions. Anybody can draw a square in a modern drawing program with a simple click-and-drag. We thought turtle graphics would be dead; that was part of the impetus behind giving them costumes and using them to tell stories. But it turns out kids are still excited the first time they draw a square in (insert programming language here)! And squirals are just as magic as ever. Fractals, too, although computers are now fast enough to draw Mandelbrot sets point by point, so you can program more beautiful ones, using programming techniques that don't illuminate recursion the way trees and Koch snowflakes do.
I guess I'm saying that really redoing the list in the spirit of the original requires paying attention to "what do you learn by doing this?" For Papert, it was all about mathematics. Turtle graphics teaches finite differential geometry. Concrete poetry teaches production grammars. And so on. Of course the twenty things were also supposed to be fun!
So my list wouldn't be all that different. The currently exciting math has shifted to some extent, from geometry to statistics, because of machine learning. So AI projects would be good, preferably projects that really teach a simplified but honest understanding of computational neural networks.
Robotics, too, would still be on the list but maybe in different forms. FIRST has raised the bar tremendously on the hardware side. My (third-hand) understanding is that their teams do the software side with a lot of copy-pasting, and not so much understanding or originality as Logo teachers would want to see. But even in the old days, trying to drive a robot turtle up a ramp taught things about friction and, more generally, the uncooperativeness of physical reality with respect to theoretical understanding.
Kids write 3D ray tracing programs in Snap!. Personally I find that level of attention to detail beyond my level of patience (not to mention competence). But there's plenty of good mathematics in that. And it's something well beyond the speed of the early personal computers.
Music, which I rejected earlier, also has some good mathematics in it: the Pythagorean investigation of musical intervals as rational numbers. In Jeanne's work, as I recall, the notes were taken as primitive building blocks, not looking inside the sine waves. I'd be happy with a music microworld that taught the beginnings of music theory.
Sorry, this isn't the list-of-20 you wanted, but some musings about the underlying purpose.