That's a good one! You're a man after my heart!
First off: Wirelessly? You are dealing with wireless frequencies already--VHF/UHF. Since you can't run RG6 coax throughout, put another HD broadcast tuner box in the attic with your antenna with an RF remote control, and add a wireless video baseband(component video & audio) wireless transmitter/amplifier onto that.
Otherwise, you're taking about an antenna repeater-- if there is such a thing for this.
I have Dish Network for HD programming. They do not provide local HD channels. I can pick the local HD channels up with "rabbit ears" using the TV tuner (the Dish HD receiver appears to have a less powerful tuner and I cannot get all the channels thru it); however, I'm not happy with the appearance and would like to use the Dish receiver to eliminate having to change inputs on the TV. Is it possible to mount an antenna in the attic and wirelessly transmit the signal to a device connected to the off-air antenna port of the Dish HD receivers. I would need a device that has the ability to support at least 2 TV sets and would like for it to support 3. When I built the house, I did not realize that I should have prewired 2 coax outlets in each room where I wanted HD programming and do not want to drill holes in the floors and wall. Are there any reasonably priced solutions? Thanks in advance for your suggestions.