I made a website just after I woke up this morning. I used Weld.io, a new service that aims to make designing websites easy and fun. It succeeds in both of those objectives, even if what you produce may end up a little rudimentary.
It’s not perfect and it takes a little time to get to grips with it, but I’m impressed by this version of the service and anticipate it getting better over time. It’s certainly worth checking out.