I have been using a Garmin Etrax GPS for years now. The unit is hand held, designed for walking and will register speeds as slow as 0.01 MPH. Garmin does not make them anymore but I have seen used for sale under $30.
Im pretty sure Garmin still makes the Etrex models. I have an Etrex 20 and the speed/location function is pretty much useless at less than 1mph.