We had a great experience under the Galata Bridge at a restaurant called, Fish Point (Balik Noktasi). The views of the Ferries and the mosques and Topkapi Palace at night were wonderful. The food is well priced and the service is excellent. If you don't recognize the types of fish on the menu, ask them to bring the tray of fresh fish to your table so you can see what you are eating. We found the prices to be excellent and at the end of our meal a complimentary platter of fresh fruit was provided. Since the restaurant is at the Taksim side of the bridge, when walking to the restaurant we didn't have to walk through the touts that line the bridge asking you to dine at their restaurant.
http://www.fishpoint.eu/
You can get there easily from the GH by taking the funicular down and then one tram stop to the Galata bridge and then walking to the bridge. It is under the bridge (lower level) on the left side of the bridge if you are facing it from the Taxsim side.
Another fun and very unique experience is Sarnic in Sultanahmet. It is in a restored water cistern underground and it is completely lit by candles. You need reservations. Both times we were there there was a guitar player after 9 PM.
http://www.sarnicrestaurant.com/en/index.jsp Some say it is expensive but I think the ambiance makes it worthwhile. Definitely more expensive than Fish Point but a completely different experience.