Tempered chocolate spheres in advance?
Chocolate will stay fresh for weeks or even months if stored correctly.
And yes, the spheres will stay as shiny and beautiful as you made them if you store them correctly:


in a cool, dark place away from sunlight 
but not necessarily in the fridge - taking them out will lead to condensation on the surface
at rather constant temperature 
and dry.


So in short:
A large enough foodsafe plastic container in a cool cellar or cupboard, away from (sun-)light and, if applicable, curious kids, pets or others that might feast on your stash in advance. Unless you have a high humidity environment, it's not absolutely necessary that the box be airtight. But if you want to be really sure, include some silica gel packs against excess humidity.

Do not stack them like nested bowls, or you could scratch or otherwise damage the glossy surface. If you have to, place one layer in your box, cover with parchment, foil or similar, add a sheet of cardboard for stability and another layer of parchment or foil, then the next layer of spheres. 

Good luck and have a good party!