Here's a picture of the kind of hat I have in mind:
Let me refer to it as an iHat (even though I would imagine that this term is already being used out in the wide world). The top hat style—which is just one suggestion among others—has the advantage of offering a rigid lightweight structure to house both the electronic components and the wearer's skull. The size of the hat and the position of the flat screen would have to be adjusted so that it could be worn by people who don't necessarily have receding Neanderthal foreheads.
The front section of the hatband conceals an elegant pull-down keyboard. Inside the crown of the hat, above the top of the wearer's head, there would be ample room for the power source and a rich assortment of components.
To help pay for the high-tech hat, the wearer might decide—from time to time, when he's not himself working with the iHat—to display publicity in the style of TV ads, aimed at viewers seated opposite him in public transport, waiting rooms, etc. At sporting events, the screen might display the colors of the team that the wearer is supporting.
Interesting and beautiful variants of the iHat could be designed for special occasions, such as weddings or horse races of the Ascot kind.
Naturally, people wearing particularly exotic iHats equipped with high-powered electronic devices emitting intense electromagnetic radiation would be advised to have their brains scanned from time to time, just to be sure there's no damage.
It would be advisable to secure the iHat to the wearer's neck by some kind of metal chain or cable. It would be silly if a valuable iHat were to be blown off by the wind and crushed by an automobile, or grabbed by an evil strike-and-run hat thief.