You can have a system that will display anything that you can see on your computer screen. Many portable computers already have the composite video output connector, often it looks similar to the external mouse or keyboard connector, except for having seven pins. Or purchase a scan converter, VGA in and composite video out. Then the "TV modulator" gets the composite video and the audio from the computer earphone connector. Set the modulator to channel 3 or 4 and you are all set. If the rabbit ears on your TV set are connected, connect a similar pair to the modulator and you are good for a few feet of broadcast range. If not, use a piece of cable to connect it to that Balun on the back of your set. Even Radio Shack has sold those modulators, so that is one more potential source.
I have three analog TV's at three different locations out in the country. I have the digital converter boxes connected to the analog TV's and everything works fine. Because of the distance from the TV stations, I use outside antenna's but if you are close to the TV stations, a set of external rabbit ears, available at most Radio Shacks, will work fine.
As far as connecting other sources to old TV's others have mentioned the RF modulators. They to are still available.
There still are some low power stations in analog. Nothing you'd want to watch, probably. We use a converter on our old boob tube and it works fine. Puts out a channel 3 signal. They sell them online, but are a staple of garage sales.
Or, you could put a 7 inch tablet in place of the CRT guts. That would be cool.
Max,depending on the strength of the digital signals in your area and the construction of the building you're in, the rabbit ears may work as an antenna for the DTV box. Just use a 300ohm-75ohm balun to connect the ears on the TV to the DTV box, and the one already on the TV to connect to the DTV box output. Hide the DTV box behind the TV, and you have a working TV, pulling in off-air signals with its own rabbit ears!