There's a lot of options here, all depending on skill level/expenses and how much time you want to spend on it.
Also: Are how are you going to receive the feed?
Wireless or wired?
I'm going to go ahead and assume that you mean wired like; Camera -> Board -> LCD.
Here's a couple of methods I have tried and find relatively easy:
BeagleBone Black (BBB): The BBB is a micro computer on which you can run a variety of OS on, like Android -Ångström Linux - Ubuntu ETC.
The BBB is community supported development platform and have the tools you need to support direct feed from a camera.
There is modules available for the BBB - to help you achieve this - they are known as capes and can be bought from a lot of different retailers.
All you need is the BBB, a camera cape and a LCD cape.
Camera Cape
LCD Cape (There is smaller ones if I remember correctly).
Raspberry PI (RPi) - RPi is a micro computer as the BBB.
The RPi has modules as well that will work perfectly well for what you want to achieve.
LCD Module
Camera Module
A personal favorite tho is the HackHD!
Why try to hack a camera that is hard to mount, hard to trigger or even hard to do anything with?
The HackHD (as the name suggest) is actually made to be hacked.
You can easily embed this camera to anything really.
And the best part is that it is very well documented.
(I really hope any of my ramblings made any sense)
Happy hacking!
Please note - I do not endorse any of the products in any way, I'm just letting you know what alternatives there is out there.