I recently had a chance to visit beautiful Istanbul for a long weekend. I stayed over at my friend's place and ended up spending most of my time in the area between Taksim square and Galata Tower. The area is good for shopping, bar hopping and sitting in small cafés. It's far enough from the touristic attractions so you can enjoy the laid back atmosphere of the ancient city in peace. Istanbul has a lot of options for night life especially if you're into dancing. I had a change to attend a swing dance and a milonga (argentine tango), both were great, such enthusiastic and welcoming people!
I love Turkish food: I's healthy, colorful and tastes amazing. Grilled eggplant, yogurt, herbs.... Oddly enough the best meal I had was a brunch in Cafe Privato . Their breakfast was a perfect combination of sweet home made fruit jams, pancakes, turkish pastry, cheese, olives, salad ... My pictures won't do the justice to the food, so here's a picture of turkish tea glass.
There are some other good restaurants and cafes nearby. For a magnificient view, try Leb-i Derya (their chocolate souffle is to die for) and Konak, which has a big rooftop café. Watch out for the seagulls! Konak has a patisserie downstairs with some delicious cakes and pastries. Here's a tip; buy a piece of cake to go and have a picnic outside!
Enough about the food, let's move on to shopping. The shopping street Iskiklal will have enough shops for one day or even two (Sephora and MAC for makeup, ByRetro on Suriye Pasaji for vintage clothes and Penti for stockings and pantyhose). If you're looking for something other than everyday clothing brands I suggest you step on those little streets that go left and right from Istiklal.
For funky t-shirts I recommend popping in Crash, "New design and second hand collection" (near Galata tower) and Harikalar Dükkani, that has all kinds of fun gifts and little stuff to bring home. Harikalar Dükkani is on really small street near Galata, you'll know you're getting close when you see white rabbits on the walls.