Have seen a good hotel, and I'm now wondering whether to do 7 or 10 nights?
I reckon seven nights would be enough for a first visit. The 'Bul can be a wee bit marmite to some folks, so go for seven and you can always come back if you both really enjoy it.
Its easy to try and see too much in one day so pace yourself.
You could spend a full day kicking around Sultanahmet, Blue Mosque, Hagia Sophia etc.
Another full day taking the tourist boat up the Boz and eating fish at Rumeli Kavağı.
Istiklal, Taksim and Galata takes another day.
Grand bazaar, Egyptian (spice) market and Eminönü chalks off another day.
Dolmabahçe Palace, Istanbul Modern Art Museum and Beşiktaş area is a day, easy.
Colwyns comment about Gulhane park is a good'un - easy walk from Sultanahmet and some nice cafes about there. North Shields pub next to the tram stop for refreshment as well

expensive but top quality. There's also Princes Islands - Büyükada is a good day out, get the ferry from Eminönü.
Getting about is easy (albeit a bit busy and cramped at times!) with an IstanbulKart that covers trams, busses and metro - taxis are also dirt cheap compared to Fethiye.
Hope that helps.
JF