Afyon (or Afyonkarahisar as it is officially called) is at an important crossorads in Inner Anatolia as it is located between Istanbul and Antalya, and between Ankara and Izmir. So if you're travelling around this region, you'll likely end up in Afyon at some point. Its Old Town is beautiful, quiet, not touristic at all, and well worth a stop if you have a day to spare.
North towards Kutahya, Bursa, Istanbul; South towards Isparta and Antalya; East towards Izmir
From the city centre, there are minibuses going to Özdilek mall and Afyum outlet, which are located at a junction where you can find lifts north towards Kutahya and Istanbul (D650), east towards Izmir (E96), and south towards Isparta and Antalya (either find someone heading straight there or ask to be dropped at the junction between E96 and D650, less than 10km, after a petrol station).