A new feature of the small television is that it can be battery powered. When you are purchasing one for your kit, make sure that the one you get allows you to put in double A batteries that you can just throw away after use. When there is no power there is no way to recharge batteries. You don't want to get stuck with a tv that only uses the lithium battery that is built into the unit. This would be disastrous and wouldn't be of any help to you in this situation.
The other thing about the portable tv is that it must be compliant with the digital signal. This means that the signal it brings in is the ATSC signal. Some manufacturers are still carrying the old system which is the NTSC and this also would be of no value to you as the current news broadcasts are not broadcasting on these air waves anymore.
Portable tvs are really the new replacements for the radio and the flashlight, as they give you both information and are a source of light. Be sure that you do not get stuck in a natural disaster without arming yourself with one of these all purpose strategies that provides entertainment as well as needed emergency news.