My first suggestion would be watching the sunset from the Galata Tower. You should plan your day accordingly, and save Galata Tower for the end of the day. It has a fantastic view of the Galata Bridge, Old City, Beyoglu, Asian side, and the Prince Islands. It offers a great view of the modern and ancient Istanbul at the same time.
Definitely check out this video:
Then, I would suggest the Maiden Tower. It is located close to Uskudar ferry pier. You can take a boat to that little island that also has a restaurant on it. You can make a reservation, if you'd like to have dinner watching the sunset.
And, also I would suggest taking the ferry from Kadikoy, the Asian side, to Besiktas or Eminonu. If you can time it perfectly, then you will be able to see the sunset over the Old City, including Topkapi Palace, enjoy the waves of Marmara Sea, and maybe enjoy a cup of Turkish tea. The ferry runs every 20mins so it shouldn't be hard to time it.
