Well.. you could simply connect both computers to the same network (preferably with ethernet, but wireless will work, it'll just be a bit slower), then share the files on the local network, and copy them over the network directly from one computer to the other.
If the files you're backing up aren't too massive in size all put together (we're not talking like hundreds of gigabytes) you could also simply archive them into a zip, rar, 7z or other archive format, and compress them while at it, this will make the file transfer from one computer to the other significantly faster (whether you do it through ethernet or using a usb hard drive/flash drive)
Otherwise well, if you don't wanna be oldschool like me, then yeah you could use skydrive, there's no need for shortcuts it's pretty straightforward, right?
If you don't want to upload them one folder at a time, put them all into one folder and upload that (or archive it into a compressed zip or rar or 7z file.) I bet if you're sane all your user files are located in pretty much a small handful of folders (documents, desktop, etc), unless I misunderstood you and you mean to copy your user account and all the crap files that have gathered up over time in your appdata folder. (That is a bad idea either way)