Since you're not running anything other than static HTML according to your original post, I can recommend GitHub Pages for you. Pretty reliable, since it's hosted in the cloud by a reputable provider.

If you want free hosting with PHP/MySQL scripting/database management, I recommend FreeHost78, I use them for my forum and it handles it surprisingly well for a free hosting service. I think for SEO friendly URLs you can enable mod_rewrite for URLs using .htaccess.

P.S. - I know this is a thread that is over a month old, but just wanted to put the word out there.