Street food you could try:
stuffed mussels
fried mussels with bread sauce
rice, chicken and chickpeas (not very exciting, but my favourite)
pickle juice
wet burgers
kokorec (intestines - not for everyone)
When my friends came to visit last year one night we did a street food tour all around Taksim, instead of going to a restaurant, we just sampled all the types of street food, with drinks in between each course.
As for fancy restaurants, I'd recommend you stick to Turkish.
You can go for meze and fish, my favourite area for that is Samatya, which is inside the old city walls, tourists don't go there and it's much cheaper than the same food elsewhere.
If you'd like to try food from the South East of Turkey, go to the kadinlar pazar area near Suleymaniah mosque - some interesting and spicier things on offer.
Have fun