Well, you could see if the website(s) in question have a calibre recipe available... and then schedule a job and have the resulting EPUBs emailed to you. Not completely independent of the PC, but at least you don't have to be
at the PC. Or you could even have this done by a private webserver -- some people pay ~$10 a month to host their calibre library on e.g.
linode so they can download from their calibre Content Server anywhere.
But otherwise, I would say looking into the dotEpub (or similar) extension for Firefox is it.