How to compute input impedance?

Calculating the input impedance by hand is almost certainly what you're supposed to do as the other answers have suggested. I just wanted to show you how to go about getting some numbers out of a circuit simulator so you could check your work (or apply the same concept to a more complicated circuit). Here's your Sallen-Key filter in CircuitLab:

And here's the frequency domain simulation showing the input impedance looking into the input:

You can open the circuit and change the parameters, configuration, op-amp model, etc. Just hit F5 and you'll see the V(out)/V(in) Bode plot, as well as the input impedance plot that I've included a screenshot of above. Using custom expressions in the simulator, like MAG(V(in)/I(R1.nB)), allows you to calculate quantities like small signal impedances quite quickly!

Using a test current source, rather than a test voltage source, makes sense for how I'd probably go about solving this on paper. However, for simulation purposes, using a voltage source as the test input allows us to more easily understand the V(out)/V(in) Bode plot at the same time.

Yes, this is a standard circuit analysis problem.

Perform the analysis in the frequency domain (R and Xc) and connect a 1A ac current source at the input. Solve for the input voltage as a function of frequency and that expression is the impedance.

I suggest using nodal analysis to perform the analysis.

Assume that the op amp is ideal and so the current into the +/- terminals is zero and the voltage at these terminals are equal.

Use the extra element theorem, as explained in Wikipedia. There are multiple paths to the solution with this approach (since any of the components may be made the "extra" one). Choosing C4 as the extra element looks like one of the simpler choices.

In your circuit, the op amp complicates things a bit, but you can write down the currents and voltages on the schematic to compute the various impedances required.

Once you've mastered the extra element theorem, you can then proceed to the generalized N-Extra Element Theorem (NEET, originally developed by S. Sabharwal), which enables you to write down the answer by inspection and a bit of algebra on the schematic:

$$Z_{in}=(R3+R23) \frac{1+s[C5(R3||R23)+C4(R4+(R3||R23)-\frac{(1+R5/R24)}{1+R23/R3}R4)]+s^2C5C4(R3||R23)R4}{1+s[C5R23+C4(R4+R23-(1+R5/R24)R4)]+s^2C5C4R23R4}$$