The travel idea
Start around Sultanahmet, then give another day to Karaköy and the waterfront. Covering both shores in one day can leave too much time in transit.
What to consider
Check tram and metro access as well as distance on a map. Compare prices after considering breakfast, room size and baggage.
Plan with more confidence
Leave space for markets and cafés instead of filling every day with museums. For children, break longer walks with short pauses.