I didn't see low cost as a requirement, so I will recommend that you buy a commercial pocket anemometer (such as
this one) cut off the unnecessary bits such as the processor and display, and wire it directly to your data logging device. It will probably take a bit of experimentation to calibrate the device, but it shouldn't be too hard (I assume that there is essentially a generator inside which creates a voltage, but it might be something more exotic like an optical encoder).