both in Greece and Turkey, being located in one single place is not really a good idea because you will consume the environs and will be looking forward to move forward. However, if that is your travel type, you should choose in between Istanbul, Antalya, Izmir, Athens or Thasseloniki since they are big cities and will satisfy you for a month. My humble suggestion will be to do one destination at a time if you are a nature and outdoor lover because being located in one place will prevent you from exploring more. Here is what i recommend for Turkey and I am sure a Greek friend will suggest a Greek itinerary as well.
Arrival to Istanbul and spend a week
Fly to Cappadocia and spend a week (walking in the valleys)
Fly to Izmir from Cappadocia and explore the west coast with a rental car like Ephesus, Aphrodisias, Hierapolis, Pamukkale and Bodrum (4 Days)
Two options to take after Bodrum; 1st; Either walk a week in the Carian way around Bodrum and fly back to Istanbul for your departure from Bodrum Airport or
2nd; drive down south to Fethiye and start walking the world famous lycian way for a week that finishes in Olympos nearby Antalya. Rest for 2 days there and explore the environs and fly back to Istanbul from Antalya for your departure.
I hope above plan looks good and dont hesitate to ask me any questions you have about my country.