I'm looking for a game that displays common state on the tablet in the middle of the table, and let's everyone muck around with their private state on their mobile phone.
Eclipse on the iPad is fun in local hand-the-iPad-around mode. But since you can't see the board while other people are mucking around, you can't plan ahead easily during the downtime.
The Scrabble app for iPad used to do that. There was a separate 'Tile Rack' app for iPhone. The iPad app for Scrabble was paid ($9.99 IIRC), but only one player had to buy it. The companion tile rack app was free. For some reason, EA seems to have removed that functionality:
http://ipadboardgames.org