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I'm the process of planning out how I want to make my very own volcanic (pompeii style) 4'x6' modular game board. Here's my plan so far:

12"x12" tiles (24 total)

8 of which will be open terrain
10 of which will be sparse terrain
6 of which will be dense terrain

The terrain itself I've got a very good idea of how to do, and I have most of the supplies. Thing is, the foundation for it I'm a little up in the air on. Should I make the base plywood or foam?

How I see it:
Foam is lightweight and I can easily create uneven terrain and lava flows; however, it is also a lot less sturdy and will require frequent touch ups.
Plywood is strong and sturdy and can handle most anything I'll put it through; however, trying to create depth is going to be difficult and the wood can warp.

I would really like to hear what people's thoughts are on plywood vs foam.

Most terrain boards I have seen are a wood base with foam upper which is then carved and cut to give vertical detailing.

That way you get the best of both worlds.

Though that may require some touch ups still, ultimately I bet that is the best solution.

I think a 1/2" thick plywood with a 1" thick foam on top would likely accomplish everything I need it to do. This is my first game board though so we'll see how it goes haha.

Any suggestions on the foam to get?

Extruded foam is the best for terrain. You should be able to pick it up from most DIY/builders stores. Get a thickness which is appropriate. If you are building a mostly flat board, get 6x4's worth of quite thin foam, then some thicker foam for carving hills out of without having to keep sticking layers of thin form together.

https://www.google.co.uk/search?q=extruded+foam+board&tbm=isch&tbo=u&source=univ&sa=X&ei=oIxmU9arJePY7Abg5oDgBw&sqi=2&ved=0CEwQsAQ&biw=1252&bih=530

Perfect, and last question for now.

I want to have totally modular tiles. How would you recommend cutting the foam into 12"x12" squares that match the wood underneath? Part of me considers gluing and just sawing the whole way through if I used a fine toothed blade. Although marking and cutting them separate should do fine as well but will take longer. Any experience on what a saw will do to foam?

Get a hot wire cutter and clamp it upright to a table/bench. Tape a 12x12 plywood/MDF square to the foam board in a corner along the two edges and then run the board over the cutter using the wood as a guard for the foam.