Distributing AV - Please Help - Newbie

Hi Guys,

I read many threads on this forum but i'm a little confused with all the choices (devices, cables, baluns, IR...) that can be applied to my problem.

I have 4 AV sources (in the lounge) all connected to a Receiver (Onkyo TX-NR-905).
I have 3 televisions in three separate rooms (Lounge, kitchen, bedroom).

The television in the lounge is connected with an HDMI cable to the receiver.
The two other rooms are connected with SD wireless transmitters.
The three televisions displays the same source at the same time.

So Far, one of the wireless transmitter is dead.
I decide to upgrade this installation to have HD video in all the rooms with at least one IR control in the bedroom.

I can run new cables in the house.

So what is the best and easiest solution to have the same source displayed in the lounge, the kitchen and the bedroom with a control in the bedroom and the lounge?

I'm definitively not a specialist of AV distribution, please could you be a little precise with the devices, cables, baluns... needed to achieve that.

(Sorry for my poor english, we do not have such great forums in France ).

Thanks. Regards.