With regards to the location - yes it's a fair way away from Sultanahmet (the old town with Hagia Sofia, Blue Mosque, Topkapi etc).
However the public transport in Istanbul is very good and very cheap, and runs until late. I found it safe and organised. The flat fare for a single journey is 3 lira.
The Bomonti looks like a terrific hotel. The DT on the European side is right next to Sultanahmet but is therefore far away from Taksim and many other attractions.
Istanbul is a huge place with attractions spread out, so I wouldn't obsess about being by the old town unless it really matters to you.
I visited 3 weeks ago - cracking place, have a good trip.
