diorama base with styrofoam

I like gluing my foam to 1/2" MDF. I use GE clear silicone to attach it. The MDF is a very stable base, it doesn't warp of flex. If any silicone squeezes out it's easily removed and it doesn't react with the foam. I would think that unless the balsa wood is really thick it would be too soft to use as a base. Gluing it to the sides would probably look better than nailing it, plus you wouldn't run the possibility of splitting it. Lattice strip would be another alternative to the balsa.

You do not want to use nails. Steel is ridiculously harder than Styrofoam® [trademark of the Dow Chemical Company], and simple thermal expansion makes a mechanical connection between steel and Styrofoam® a non-starter.

If I were combining Styrofoam® with balsa, I'd use glue, specifically Hold the Foam® from Beacon Chemical Company. You can purchase it anywhere that sells commercial Styrofoam®. Non-toxic, non-flammable, it's sort of an acid-neutralized water-based paste, almost as thick as silicon glue.

You're probably better off with some kind of stand-off (felt pads work well) between the base and whatever it rests upon.

Nails won't hold in styrofoam.  White glue will bond it to your wooden base.  You can cover styrofoam with almost anything.

I agree with Mike,,,  white / wood glue will bond with plenty of strength.

Best of luck with it

I am similar to dave in that i start with a wooden base, usually any piece of wood i have to hand. I attach the foam useing white glue. I also add a balsa wood surround to all my bases useing white glue and small tacs in the woden base.