At a technical level, JSFiddle or equivalent comes kind-of close. Set up a template with a nice big element, then you've got a simple imperative API to draw stuff which really does come pretty close to what you'd get from a BASIC> prompt.
That said, I wonder if it's even possible to replicate the C64 (or equivalent) experience. Looking back, I think a big part of the "magic" was that there were relatively few distractions. Just you, the machine, and (maybe) some paper documentation or a magazine with a few listings [1]. Can that be replicated once you're used to network-connected computers that are gateways to almost unlimited amounts of video, colourful games, etc.?
(My child is getting to the point where I wish I knew the answers to some of this myself...)
[1] I'm pretty certain type-in listings were the biggest contributor to my learning, early on. That doesn't seem to be something that comes up terribly often nowadays (although I note that Zed Shaw's "Learn Python the Hard Way" is pretty specific about telling you to hand-type in the examples...)