Are there any VCR/DVD combo units that can be directly hooked into the TV for recording purposes? That don't have to run through an external box - such as cable or Dish?

A VCR/DVD recorder takes a video input and records it. A TV takes a video input and displays it. Both need a video input. Unless you TV has a video output that you can plug into the VCR (rare) you have to use some video input. Where does your TV get your input from.

Agree with ScottGem, TV is at the end of the line.
At most basic, if you have Antenna or cable going into DVD/VCR will go out to TV.
Older Tv's do not have Audio/Video inputs, and some DVD/VCR's Don't have cable fitting to TV. You need Modulator to convert Audio/Video to a Cable output(Channel 3 or 4)
Have found these at dollar store for $12.00(RCA)