I used to play Goldeneye Online all the time a few years back (Found it through the website /u/santoscrew just linked.) I'd recommend Mupen64Plus for your emulator, but I can't seem to find a download with the GUI already set up. Here's a link for Project64 - http://www.pj64-emu.com/downloads/project64/binaries/
If you install Project64, BE VERY CAREFUL when installing, as at one point it asks to install some adware crap, just untick the box and carry on. - EDIT - Yup, it's called StrtPoint or something. Click skip then click decline on the little box that comes up.
Grab the ROM from here, http://www.emuparadise.me/Nintendo_64_ROMs/007_-_GoldenEye_(USA)/39545-download
Nintendo ROMs are getting a bit tricky to find lately, as they've been going on some sort of crusade to remove them from rom sites.
If you need any more help, feel free to PM me or reply to this post. As I mentioned I played GE on an emulator (and the real thing!) for years.