Oops, nevermind, silly suggestion. It's already been done, you just have to Google "basic interpreter javascript" to find it.

http://www.calormen.com/Applesoft/ - Starts right at the interpeter

http://www.ngbasic.com/ - Has more of the classic BASIC feel, opening a window that looks like ye olde BASIC interpreter, but requires two clicks before you can find it.

http://www.quitebasic.com/ - Also starts at the interpreter, but with a more complicated example program.