This might not be the prettiest Twitter client but I feel it is the most versatile. With separate tabs for your friends’ tweets. . .the replies to you, and the direct messages to you. The only thing that I see this is missing is the public timeline.
If there are any links listed in a tweet, you’ll see there is a blue badge to the right of that tweet. If you click that badge then you’ll go straight to that link(in it’s own browser).
I think an auto refresh and location feature would make this the best client, hands down.