it depends on ur tastes ...but my fave tree are;
1..İstanbul
2..Karadeniz..(black sea region...because there u ll find the combination of blue adn green)
3..Ephesus..(near İzmir..and there u ll find ancient relics)
4..Caphadokia ( great!)
5..Pamukkale (there is no place in the world equivalent to its beauty)
6..Anıtkabir (the grave of the best leader ever..) (in Ankara)

hmm. i think these are for sightseeing;
1. istanbul
2.pamukkale
3.caphadokia
but if u like greens u can go north of turkey especially to Ayder. there is wonderful...
if u like beach u can go both south and east of turkey. for ex: kemer. bodrum, cesme, fethiye...

I never been to Turkey but there are some cities there I want to visit:
Izmir;
Ephesus;
Ankara;
Antakya.

hmmm there re many places to go.. but you want just 3 places and these should be near istanbul.. then; Çanakkale, İzmir and Bursa..

ı think olimpos is the best than kapadokya and sümela