is there a free online website builder that also provides a free domain name?
In-so-far as free, (along with a free sub-domain name) there are two that I recommend highly. (Not in any particular order).
The first is Webs.com Webs has a new easy to use site builder (SiteBuilder 3). It has a smaller learning curve than most other site builder programs and you’ll be up and running in no time. Everything is free, but Webs does have forced advertising.
The second is Wix.com At Wix, unlike Webs, you’ll have the option to build either, a regular website or a flash website. Their HTML-5 Web Builder program is also very easy to master – and has more features than the one at Webs. Their flash web builder is just as easy, although it will take a little time learning where everything is.
Plus, Wix has no forced advertising other than a small button which when clicked, takes your visitor to the Wix home page – to build their own free website.