This sounds great Vitor!
I would add diffusion too. It is a completely different formulation.
Also you might want to try 1st and 2nd order elements.
Do you know the story of the chess checkerboard, right? After a n ideas one ends up with 2^n runs.
Use the 3dshape but stick to geometries with analytical solutions, i.e. sphere, cylinder or prims.
Then you can use the bunny.
My candidates for paralellization are the routines that compute the elemental matrices (both in diffusion and SN) in FEM and the routines that find neighbors and the ones that build the big matrices in FVM.