I use
www.blogger.com
You can set it up so that the blog is completely private, so that only your username can access.
Since blogger is owned by google, it also means you can google search from within your blog. (It is completely private and will not appear on a normal google search ever or to anyone, as long as you set your blog to be private - "Only blog authors" is the setting.)
There are others available as well, that's just what I use.