We have this now with services like heroku and Google App engine.
Heroku is probably the easiest to get started with and is generously free (you can run actual sites from that free instance). At work when we were mentoring a boss's nephew we had him going to Michael Hartl's Rails tutorial and he had a site up on heroku in about an hour and was really have a great time seeing things iterate as he pushed up changes.
You don't get newapp32.codeacademymeetsgeocities.com but you do get something like rushing-waterfall-2311.heroku.com and you can customize that rushing-waterfall-2311 should you care too (still for free).
Heroku is probably the easiest to get started with and is generously free (you can run actual sites from that free instance). At work when we were mentoring a boss's nephew we had him going to Michael Hartl's Rails tutorial and he had a site up on heroku in about an hour and was really have a great time seeing things iterate as he pushed up changes.
You don't get newapp32.codeacademymeetsgeocities.com but you do get something like rushing-waterfall-2311.heroku.com and you can customize that rushing-waterfall-2311 should you care too (still for free).