I think Turntabulator is pretty good for speed. Some other apps will calculate wow and flutter, but those don't give similar, repeatable results. One issue with testing is the accuracy of any test record. You may end up measuring how well the test record is centered rather than the wow and flutter.
That said, WFGUI app is free and works with standard test records. I have a two test records and can set speed based on a test tone. As mentioned, Turntabulator is very accurate. Get a sponge or something you can center, poke a hole in, then center you phone as best you can over the spindle. Certain platter/bearing designs are more susceptible to off-center weight.
I use WFGUI for final adjustments.