Visit Taksim Square
For a more lively part of Istanbul, Taksim Square and the shopping street leading up to it are one of the best places to stroll around and spend a day shopping for souvenirs or trying out all kinds of street food. The shopping street gets really crowded in the evening and the restaurants, cafes, and bars will be filled with people winding down for the day. It is a fun and lively area that contrasts with those you saw before in the old town area.
You can also take photos or even get on the iconic red Taksim heritage tram that connects the Asian and European sides of the city from here. The tram operates between 6 AM and 12 AM every day and it should be difficult for you to track it down once you are on the Taksim shopping streets.