If I have a HDHomeRun hooked up to the iMac in one room and a TV in the other. How can I change channels on the TV in the other room?
Please clarify: are you saying you are watching the EyeTV content from your mac on the TV in the other room, and want a handy way to change channels while watching the TV without walking over to your iMac?
(ie: Do you mean that you are somehow streaming the iMac's EyeTV content to the TV in the other room? Are you doing this through Apple TV Airplay Mirroring? Or do you just have the mac hooked up to the TV via AV cables?)
If I understand correctly and you are watching the EyeTV content on the TV, then you are basically just looking for a way to control your mac without being in the same room. For that, you have a couple of options:
1. If you have an iDevice (iPad, iPhone, iPod Touch), then check out apps like Rowmote and AirMouse. Both allow you to control your Mac over wi-fi using your iDevice. I like AirMouse because it basically makes your iPhone into a remote trackpad and this would mean when you are watching your mac's mirrored screen on the TV you can see the cursor move on the screen as you control it from your iPhone. Rowmote is good two, and simulates an Apple Remote, so may be more appropriate if you are mainly using it to control EyeTV. I have used both for exactly this purpose and it works fine. Just a few bucks for either app. There are other apps that actually let you see your mac's screen on your iDevice, which is overkill for your purpose, but theoretically would work. example: splash top, VNC, etc.
2. If you don't have an iDevice, you could pick up an RF remote for the mac, like this:
http://www.amazon.com/Remote-Front-Row-Mac-Only/dp/B000FBK3RE These remotes are not IR, so they don't require line-of-sight, but their range may not be great, so it may not go through walls. (read the fine print: some are more powerful than others and hence have better range).
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You will need a media extender connected to the TV. The cheapest is a XBox 360. You also have to have Windows Media Center running on a PC/Mac.
Actually, the cheapest media extender is almost surely a refurbished Apple TV, at $85 plus tax, with free shipping.
http://store.apple.com/us/product/FD199LL/A