One could easily argue that the Final Fantasy series has some of the best music to ever grace video game consoles. Why not gift a Final Fantasy fan with an OST or two of their favorite Final Fantasy games?
You should be able to find any major Final Fantasy game OST online somewhere, especially in places like eBay and Amazon. Depending on how all out you want to go, they usually range from a basic CD around $15 to something grandiose, boxed, and fancy which could be as high as $50-plus.
Also, don’t restrict yourself to plain old OSTs. You could do a mixtape of the best remixes out there on the internet or purchase an orchestrated remaster such as the Distant Worlds collection. Don’t rule out giving them some music for a game that maybe they never played. Final Fantasy XI in particular was missed by many fans, but still has excellent music from the famed composer Nobuo Uematsu. Finally, if someone on your list has been very nice, you could get them the 25th Anniversary Ultimate Box. I’ll reiterate, VERY NICE considering the price it’s currently going for.