OK, on the target machine I selected "Design".
Got a few errors, republished the template, and it seems to work on the
target machine.

Thanks for the help.

The InfoPath SDK, I beleive, has a tool that will allow you to reset the
publish location for a form, but why not try this first:

Right-click on the .xsn file and choose Design.

I have started creating some forms, both at work and at home.
When I try and move the forms, they will no longer open, giving errors about
"file name or path is not valid".

Isn't there a simple way to copy a form template somewhere else and use it?