My car is a 2004 G35 Sedan - the emblem that says "G35" on it has been stolen (before I bought the car) - I'd like to get a new set, but I'm not sure where on the trunk / rear it goes. I've seen some on the passenger side below the tail light (not on the trunk), and I've seen some on the passenger side above the tail light (on the trunk).
P.S. I'm in America so the passenger side is on the right hand side when driving.

I've always seen it in the right side, it probably wasn't stolen it was likely intentionally debadged. If it was stolen there would be a ton of adhesive residue it doesn't come off easily it takes a lot of solvent and time to get it all off.

Yes, debadging is a thing - done with a heat gun I believe. Some folks think it looks cleaner. I think the original location was under the right tail light, like this:

I believe there is a thread (sticky even?) With all the measurements for rebadging all badges for all models.

Personally, I'd leave it off. If you don't know where it goes, there isn't any ghosting where it used to be. Looks better debadged, IMO.