1

Hi - and welcome to Thorn Tree.

Six flights a day from Izmir to Istanbul (Sabiha) with Pegasus.
Fares from around €20 one way.

2

Welcome to the forum Hourglass.Flights vary in price greatly.I don't know your travel dates but looking at flights this week and next they are around 70/80/90€.This is Kayseri to Izmir which is covered by Sunexpress and Pegasus airlines.
You can take an overnight bus direct from Göreme to Selçuk if you wish,no need to go into Izmir.This one from Metro commences in Kayseri,passes through Göreme at 20.15 arriving in Selçuk at 09.45,cost 60TL(25€)
https://online.metroturizm.com.tr/BuyTicket.aspx
and this one too with Nevşehirliler Seyahat leaving slightly earlier at 20.00,same price.
http://eticket.ipektr.com/firms_41/Kara2.aspx?881906890872892909884900884934956930921896890866912905862922884934947930887862890888884906934893871915907871879883903930915862904884906934905872890868912888930909862904884880934948953976871922890914890976948956947948976899872904908872892864872930916934951948949861

Flights between Izmir and Istanbul are almost as frequent as buses as the route is covered by all carriers-THY;Pegasus,Anadolujet,Atlasjet,Onurair.The last two carriers are worth an extra look as they provide a free shuttle from Selçuk town centre to the airport,saving you a little bit of hassle :)
Again looking at next week there are plenty of flights from Izmir into Istanbul Ataturk airport for 70-90TL(30-40€).

3

Thanks! That's awesome info.