Joelcbonaldi, you have 3 options:
Once you have arrived either airport you can take a transfer to Ürgüp using these guys
2. day or overnight bus from Istanbul to Ürgüp. There are multiple bus companies that offer this service. You can purchase the tickets from Istanbul otogar (bus station) or bus ticket office in Çapa-Şehremini near Sultanahmet on the day of travel or a few days in advance in person like all locals do.
Journey takes 10-11 hours and tickets cost 60-70 lira.
3. High speed train from Istanbul (Pendik) to Ankara which takes 3 hours 45 minutes and costs 70 lira.
Then take a bus from Ankara to Ürgüp which takes 4 hours and costs 35 lira.
Joelcbonaldi, there sure is a lot to see & do in Ankara.
The city has a great castle with many museums, mosques, eateries in and around it.
There are hourly buses from Istanbul to Safranbolu which take 6 hours and cost 60 lira.
From there take a bus to Ankara and then a bus to Ürgüp.
Tks a lot!