Let's start from Taksim Square, it is consider the beginning of modern Istanbul. A square full of history of strikes, movements... You can see the Monument of the Republic opened in 1928, just at the back of the metro station is the Ataturk Cultural Centre. Right now you can't have any demonstration here, but you can in the area and they end up here too; you'll see policemen around for sure.
This is the Monument of the Republic
For us it is also the beginning of Istiklal Avenue, it's not a street I would recommend, there are only shops, but it is also a place to wander around to get to our final destination. You should know two things about Istiklal: it will never be empty and you should see/get on the historic tram built in 1956. It's not bad to get to the end of the avenue and its cost is as any other public transportation, but the truth is that with the amount of people walking around and that ignore the tram's bell, it's not fat. At Istiklal Avenue you mix tradition with modernity, in its surroundings there are lots of restaurants and pubs.
At the end of this avenue you'll find a street going down which would lead you to Galata Tower, it is full of small and themed (musical instruments, towels, souvenirs) shops. Half way that street to your right you'll find Galata Tower. This tower was built in 1348 and for many years it was the highest building in the city. Today you can still enjoy its skyline from the Golden Horn (although it is more hidden). It wouldn't be rare queuing to get in, you can go up to the seventh floor with the elevatir where you'll find a nice restaurant, if you keep going up there is a cafe and a 360 degrees terrace... What a view!
To finish this trip, you just need to cross Galata Bridge, its views, its vibe and the constant smell of fish while you cross the Golden Horn. The bridge you stand on was built in 1992 taking the place of the old bridge built between 1909 and 1912. In the lower part of the bridge there are lots of restaurants and at the end, getting to Eminönü you find boats that serve fish sandwich, from the far they look like carousels. A walk while the sun is setting, because the light is beautiful at that hour, is impressive; in any way, the walk is a must because of its beauty.