If you stay in Sultanahmet, you'll be only
steps from Istanbul's major sights, including Ayasofya,
the Hippodrome, and Topkapi Palace, but you may
not get a swimming pool or Bosphorus views.
If you stay in Beyoglu, especially Taksim
Square, you're close to shopping and nightlife,
and only a 15-minute taxi ride from Sultanahmet.
Your hotel will probably offer a swimming pool and
Bosphorus views.
If you stay on the Bosphorus shore, you may
have both these features, but there may be few shops
or attractions near your hotel and you'll probably
spend an hour or more each day getting around by
taxi.