Izmir - Denizli buses are now only lasts 2.5h, thanks to the new highway. From Denizli city centre to Pamukkale is 15 min by taxi or 30 min by local buses/dolmus.

Izmir - Selcuk dolmus (1.5h travel time (one way), first dolmus at 7am. See link for timetable
See www.ulasimsaatleri.net

take a bus from Izmir to Nazilli (over 60 buses daily, travel time around 2h. check: obilet.com for bus schedule) From Nazilli, there are frequent dolmus to Karacasu (45-60 min), and from there there are direct dolmus to Aphrodisias (15 min).

There are some infrequent direct buses to village Sart (1.15 min) or more frequent buses to Salihli (1.20 min) and local dolmus from Salihli to Sart (15 min)

This may be a stretch on public transport, but easy by car and a short distance: Izmir - Seferihisar (Sigacik-Teos) dolmus lasts around 1 to 1.5h (first at 7am). Ferry to Teos to Vathi is at 8 am and lasts around an hour. From Vathi port to Pythagoreio is 11 km. Ferry returns at 5 pm

Izmir - Bergama dolmus (1.5h travel time (one way), departs at every 20 min)

Nea Moni of Chios: Izmir - Cesme bus ("Cesme Seyahat" bus) lasts around 1.5h. If you catch the first bus at 6.30 am, you can easily catch all the morning ferries to Chios (17 to 40 mins depending on the ferry). From Chios port to monastery is 11 km by taxi.
See cesmeseyahat.net