How can you identify which are the strongest PhD programs in particular subfields?
Two suggestions:


Look at the research publications of faculty in your area of interest and then look for the most widely cited research in this area.  You can easily find such information using tools like Google Scholar.  Then find out where the authors of these widely cited papers are teaching.  
Look at what happens to graduates from the different programs.  Many faculty have web pages that list their recent PhD students, some universities publish graduation programs that include lists of graduates, and there are sometimes other ways of identifying recent graduates of a particular Phd program.  If you can't find those people on the internet, that's a strong indication that they working in academic careers.  If you find them but they're teaching at community colleges and regional comprehensive universities, then that tells you a lot about how well the graduates have done in academic careers.