There's a reason the world has transitioned to HDTVs. It's not that there was anything wrong with the concept of the television, it's just that the old giant boxes that occupied so much space in our homes were entirely the wrong shape for the task at hand. A giant cube with an antenna is a design that begs to be portable in a way televisions never have been. That's why the form-factor needed to move into a new market, and that's what makes the Smart Cube such a good idea.
While there seems to be no shortage of Twitter clients on the Google Play store, they all seem to be a mixed bag of different features and reliability. Some will do push, while others are free; some won't do notifications, and some animations are downright sluggish. Sadly, unless you have the time to go through every app to see which one fits the best, you'll likely need to settle for "close enough."
Echofon looks to add one more to the pile with the beta of their popular client.