Well, none of the bridges over the Bosophorus are open to pedestrians except during the Istanbul Marathon. The next one is November 11th 2012. I missed it this year due to rain and being super lazy, but even driving over the bridge is amazing, so I can't imagine how good it would be to do it by foot.
If you'd accept a slightly less august bridge, the Galata bridge, stretching from Karakoy to Eminonu, is quite nice. It's bi-level, offering you two options: On the top you can see a ton of fishermen chilling out and trying their luck, and you can appreciate the dichotomy of the new and old cities different building styles. The bottom has a ton of fish restaurants and some of the most aggressive touts in the city, all of whom will ask you to come in, eat a fish, or drink a beer. A lot of those places are pretty nice, and chilling out and looking at the water is a pretty nice way to kill some time.