LÖVE

Where might LOVE be installed at on those platforms?

I am creating a LOVE utility tool but only have access to Windows.

On OS X it can be "installed" anywhere. The .app is completely self-contained. /Applications/ is a typical place to put it, but you really can't rely on users doing that. I have several usable copies of LOVE in both my Downloads and Documents folders.

On Linux, if it's packaged with the distribution or the official packages, it will be on /usr/bin/, otherwise it depends on the package or the person who installs it but a common place is /usr/local/bin/.

That's only valid for the love binary itself. The libraries are installed elsewhere.