We picked up a 7" TV that runs off 12v, an internal battery or 110 (which also charges the battery). The brand is Axion, model AXN 8701. We picked it up on a "rewards" with a credit card we were about to cancel, so the cost was zip.
We used a different 7" TV on Wild Blue for the past couple years, but it wasn't digital. 7" may not be big enough for most folks (we now have a 16" on the boat), but this is a decent little TV. The internal battery is good for a couple hours and has to be plugged into 110 to charge (doesn't charge off the 12v adapter). It has an external antenna and auto tune to scan for channels. The picture is good (when the reception is good), the sound is a bit tinny, and it's easily portable.
Last year, when we were looking for a 12v TV with a digital tuner, the pickin's were pretty slim. No idea if that has improved since.
Best wishes,
Jim B.