Where is the 'Where from' meta data stored when downloaded via Chrome?
It's stored in an extended attribute on the file. Specifically the com.apple.metadata:kMDItemWhereFroms attribute. It may stay with the file when you move it to different computers, but it depends on the filesystem or file sharing protocol you use. If you move it to another Mac on an HFS+ disk, it will likely keep it, but not necessarily if you transfer over the network, and most likely not with an external disk with a non-HFS+ filesystem.

You can check a file by running xattr -lp com.apple.metadata:kMDItemWhereFroms myfile in the Terminal, or remove it with xattr -d com.apple.metadata:kMDItemWhereFroms my file. ls -l@ flag is also useful; it will list the names of xattrs along with the usual ls information.

If you want to remove it from multiple files, have a look at this question: How to remove xattr com.apple.quarantine from all .webarchive files with that extended attribute?