Sultanahmet is very touristy and in the face, its crowded and not something you would really like
But at the same time it has a lot to offer and hence all of the above.
The district is very convenient from a transportation and amenities point of view.
Traffic both pedestrian and vehicles could get a bit crazy especially during the season.
If you decide to stay in nearby hotels or pensions, expect to walk uphill most of the time, and the hotel would mostly lack an elevator.