My best recommendation is to stay in Sultanamet rather than in the new city. We have stayed at the Yesil Ev on two of the visits and love the location as it is between the Blue Mosque and the Haigha Sophia. It is an old touring hotel, as is the Pera Palas, and is actually a green house. If you see pictures of these two famous monuments, you may be able to glimpse the Yesil Ev between them.
Cappadocia is a must and a trip on the Turquoise Coast is highly recommended, but a limited time in Turkey is a problem with seeing both the country and Istanbul. We are not city people, but that one is at the top of our list.