Lots of threads on this topic. Here's a link to one that contains links to a number of others.
http://www.smwebhead.com/phpBB3/viewtopic.php?f=19&t=7123&p=68907&hilit=+tv+install+#p68907Couple of things to consider: (1) location; and (2) how you power it.
As to location, ,many here (including me) don't like the location where the mirror is. Not the easiest place to view, especially if you're laying down for the night to watch a movie or a show. Many like above the aft cabin or on the wall to the head. I prefer the wall to the head.
As for power, you can pick up any 120v set from anywhere and power it off an inverter. This gives you far more options at less expense than buying a straight up 12v tv. There are also some standard 120v tvs out there that have the the converter on the outside built into the chord. In other words, the tv internally runs on 12v, but the converter on the outside allows it run on 120v when plugged into a household outlet. Simple fix - just cut off the converter and hardwire it into the boat's 12v system. Only potential hangup with this is that some on the forum think that some of the tvs made for household use don't or can't handle the voltage fluctuations in a 12v system on a boat. I don't know whether that's true or not, but something to consider. If you're worried about it, you can pick up a tv designed to run on 12v from any number of RV websites. I have a 12v Jensen that ran me a little over $300.
Good luck with the install and post some pics.