My entire music collection is gone from Finder I do not use iTunes but instead store my music files in nested folders in /Users/User/Music. I recently downloaded Tomahawk, a music player. 

I decided quickly that I preferred to stick with VLC for playing music, only to find that I can no longer use VLC as all my files are removed from my music folder. I restarted, and some of the files appear in Tomahawk program while other are gone. It seems unlikely (and would be very unfortunate) if the files have been totally deleted; I imagine they are hidden somewhere on my computer. Where can I find them, and/or is it possible to reset my system to a few hours ago or restore them in some other way?

Note: it is not the entire folder that has been removed. The folder structure (subfolders for each artist, etc.) remains, and other files, like images of the album covers in .jpg format, remain.
It seems unlikely it would delete them, but I don't know how that app works at all...
...so, assuming Tomahawk has moved the files to its own cache/storage location, you could try using something like EasyFind (freeware) - which can search hidden locations far more easily than Spotlight - to look for either Folders containing the name Tomahawk, or one or two actual music file names.  

Chances are, you find one, you've found them all.

Without Time Machine as a quick revert, moving them back to their original locations may not be so simple - it might be a case of dragging each one back to its correct folder, one at a time.