Maybe mirroring isn't the solution. Why are you getting blocked? Even a Geocities free account should be able to handle one page unless it's got a LOT of stuff on that one page...or a LOT of people are using it.
If you're thinking about having multiple accounts and keeping mirrors that way, free webhosts usually frown on that, but the best bet is to make an entry page that has nothing on it but the title and a link to whatever you want to use as your page. Add additional links to the entry page for each mirror page. Otherwise, mirroring won't do any good if you just link it on your main page (the one you're mirroring)--once you run out of bandwidth on your main page (index.html), no one will be able to follow additional links on your site.
If you just want to be able to see the site yourself, make a copy of the site on a floppy or CD and keep it with you.