A practical op-amp connected in a unity gain configuration will have a very high input resistance (mega-ohms or higher). How can I add an external resistor to modify the input resistance to the kilo-ohm range (while keeping the output resistance low)? Can I connect a resistor between the inverting and non-inverting terminal?
A resistor from In+ to In- is not ideal to lower input impedance. It increases noise and has a capacitor-like impedance due to the feedback that constantly eliminates the voltage across this resistor. Its DC impedance will be very high.
To get what you want, add a resistor from In+ to a fixed voltage node, instead. E.g. to Gnd or to one of the opamp supplies.