I don't know about Google's free websites, but those at x10hosting.com are completely ad-free. They do have a perhaps-not-expected requirement that you must log on to the forums at least once a month (ostensibly to read system announcements) to keep your web site from being marked inactive -- this lets them keep their system reasonably free of "zombie" web sites that people set up, lose interest in, and then leave forever.
(They also have an option wherein you place ads on your site and they give you more bandwidth in return, but these days you have to specifically ask for it -- so many people couldn't figure out how to or didn't actually place the ads that they don't even advertise the option anymore!)
What are you using to generate your web pages now? Fundamentally, you need to (1) generate .html files and (2) upload them to the web server. (1) can be down with something as primitive as notepad, but there are plenty of freely available fancier solutions -- even OpenOffice can save documents in HTML these days. (2) is the least of your worries -- FTP clients come with all modern operating systems, and fancier means (such as WebDAV) are freely available for all contemporary OSes too.
That I don't know, although I can say that x10hosting doesn't really qualify. They have a "web page builder," but it's really meant more to get a "skeleton" or "coming soon!" web site up and running rather than to provide a full-featured interface to maintain web pages.
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