My only real exposure to the KIM-1 back in the day was kibbitzing while Joe DeCuir tested the first-silicon TIA (custom chip for the Atari VCS). Recently I was given a wire-wrapped one (not yet photographed or played with, I have some respect for its delicate state), but mentioning how useful it would be to have a reference sample ended up with my being given a fully built one. Here's what I've done so far.
The workbench where I am setting this up for now. KIM on the right, a CIT-101 on the left, with an orphan iBook standing in for the VAX-11/780 I would have used.
Kim can be used mostly stand-alone, with I/O via a calculator-style keypad and six-digit 7-segment display.
Or, you can flip the switch and use the Teletype™ interface, which I had to adapt to that new-fangled RS-232 for connection to the CIT-101.
Not a great shot, but this is what TTY mode looks like. Interaction with KIM at the top, and a login prompt from the iBook below. Note to the curious, TTY support for real serial lines seems to have rotted a bit on MacOSX. Gory details some other time.