We went in November 2012, and stayed in an apartment in Beyoglu, near the Galata Tower, the company we booked through was xflats. This was a great place to stay, everywhere was pretty much walkable, and there are trams if you fancy it. There is an Istanbul card you can buy if you want to go visit a number of the touristy attractions, we didn't get one but it looked like good value, and you can skip some of the queues if you have one.
Food-wise, the two vegetarian places we tried were disappointing (Zencefil and Parsifal). Our best meal was when we took a ferry across the Bosphorus to Kadikoy and ate in this place: http://www.tripadvisor.ie/Restaurant_Re ... anbul.html
They have a bunch of cold mezze you can choose from (pay by weight) and things were either fairly obviously vegan or the staff were helpful pointing out what was good. They also have a hot counter, where my (omni) husband got a couple of dishes that turned out to be accidentally vegan (or at least looked vegan to me), they were really good too.
This little cafe: http://www.happycow.net/reviews.php?id=29048
was nice, it was very small, the service was pretty slow, but the staff were very nice, I think I had a breakfast of tomatoes, cucumber, bread and olive oil (they even checked teh bread was vegan), my husband had a scrambled egg thing he enjoyed.
We had good falafel, but I can't remember where!
We also went to a really nice Indian restaurant with a view of the Hagya Sophia from the third floor, can't remember the name but if I come across it I'll let you know!
This blog is useful: http://veganbackpacker.com/blog/turkey- ... an-travel/
There were little carts everywhere selling simit (bread like a pretzel) and roasted chestnuts and different kinds of nuts, and fresh squeezed pomegranate and orange juices. Outside of Istanbul I tried gozleme and pide (veggie versions without cheese), both very tasty.
The Hagya Sofia, the palace and the Basilica Cistern were all worth going to see. If you go to the palace, you can pay extra to go into the harem, which was weird but well worth it. Go to the Basilica Cistern early to beat the crowds, it's very cool when there are only a few people there!
Hope that helps!