Here is what would be reflected.. It's the room that people come into from the front door

My husband has been begging for a tv over the fireplace...

one more thing to consider, you can see the the way the lights hit the wall, it will reflect off of the mirror depending on the size of it.
In general, I would put a mirror about 50% of the width of the fireplace, mantel to ceiling (leave a couple of inches wall space)

You need to also think about orientation or shape of mirror too. You can go horizontal, vertical or even round.

I've seen a TV that's been used on some of the home improvement shows that when it is off looks like a mirror. Could be a way to make both of you happy.

This is double post. :)

Does it have to be a mirror? The ceiling lights above the fireplace would showcase a framed piece of art beautifully. The lights bouncing off a mirror might be odd. Whatever you decide on, I would go rectangular.