Topkapi Palace covers a large site, and knowing that in advance changes how you plan the visit. Four courtyards run one after another, with the Harem branching off the second; seeing everything without hurrying takes about four hours.
Practical points: tickets for the palace and the Harem are separate, queues are shortest in the first hour after opening, and there is very little shade in the outer courtyards during summer. The Treasury and the terraces overlooking the Bosphorus are the two parts nobody should skip.
From Hotel Yasmak Sultan the walk is around ten minutes, either up through Gulhane Park or along the tram line past Sirkeci. Coming back downhill afterwards is easy, which is why most guests place Topkapi in the morning and keep the afternoon lighter.