"Back in the day" the BASIC language made sense, as it was right at your prompt in text based interfaces. The same situation today is the web browser, and the ability to open up the developer's console and getting direct access to a web site's JavaScript, html & CSS. Forget BASIC, and introduce your kids to web developing. They will "get it" much faster than "boring dumb BASIC, can't do web stuff, it sucks."
A huge part of the appeal of C64-style BASIC is the lack of distractions. I mean, you're already talking about CSS! :-) A better match than Javascript (which doesn't have an interactive console, and HTML+JS is event-driven) would be Python.
node.js has a text console if you don't want the web browser attached.