What files does the GECK need to run and make mods? I want to copy just those to another computer to make some things but dont want the whole Fallout NV game on it.

Given you'd need the resources in the BSAs, you may as well just install the whole game a second time. It's on Steam, so there's no issues with that.

You need the whole game though. The GECK is basically just the interface of the editor. Aside from that you need the some DLL files, and all the BSA files, and some other things, which basically equates to the whole game. Plus, how would you test what you made without the game?

For a 'clean room', you need:

• FaceGen\SI.CTL
  
• Meshes\Sky\Stars.NIF
  
• Shaders\*.SDP

Then you can switch directories by renaming 'Data' to ';Data' to '-Data' or whatever...