I was giving this project some thought. My thinking is:

LED arrangement similar to what the OP proposed (you will need a mortgaged LED if not already mentioned).
LEDs to show board position as someone proposed,
LCD for Chance and one for Community Chest each having its own MCU. A button to select a "card". What would be really cool if you used graphics displays to show scanned images of actual cards.
A LCD/MCU for each player to show their bank account.
The banker would have a MCU with keyboard to arrange payment to and from players. Payments between players would take place through the bank to make things easier. Or if you really wanted to go crazy have a touch pad display for all players.
LED dice as mentioned.
All mcus would communicate via SPI or similar bus.

 

Thanks everyone for your input. Heading down the modular route. Will post pics as the project progresses.