TweetDeck has released an iPad optimized application with an interface that shows you everything you want to see at once
Features: - multiple columns - multiple twitter accounts - reply, retweet, direct message and favorite from a tweet - view user profiles - see recent updates and who a person is following and being - followed by - follow or unfollow and block or unblock a user - add All Friends, Mentions and DM columns - add Search columns - add Trending Topic columns - add Twitter list columns - both lists you've created and those you follow - cross post updates to any combination of your accounts - geotag your tweets - shorten URLs - access your Twitter contact list - upload photos (from the on-board iPhoto library) - rearrange columns however you like and delete those you no longer need - view geocoded tweets on a full-screen map
Note: Version 2 will have much closer parity with Desktop TweetDeck including full Facebook integration, notifications and some more superb real-time visualisations.
You can download TweetDeck for iPad from the App Store for free.