Hamdi Restaurant has excellent food, a fabulous view and isn't terribly expensive. It's located just adjacent to the Eminönü Ferry Terminal/Galata Bridge/Egyptian Spice Bazaar. It's just across the plaza from the ferry terminal. It's nearly impossible to miss at night as its name is written in big, blue luminous letters--just look up as it's on the top floor of a large 5-6 floor building. I highly suggest reservations as it is well known and popular.
While pricey and with food that's not Turkish but definitely influenced by Turkish cuisine, Can Oba Restaurant has delicious food. It's in Sirkeci (quite near Eminönü ) just off Ankara Caddesi. Reservations for dinner are utterly required and it may well be impossible to get them at this late of a date. Lunch is also served--no reservations required but it's not the sort of high cuisine served for dinner.
Hidiv Kasrı has an awesome garden setting and serves and excellent breakfast/brunch. It's on the Asian side past the 2nd Bosporus Bridge. You really need to take a taxi for the last mile or so up to the place as it's very steep and also very difficult to find. Sunday Brunch is especially popular.
There are so many very good restaurants and so few bad ones with so many of the very good ones also very reasonably priced that it's hard for me to make suggestions for specific places. (It's also very hard for me to remember the name and exact location of many of the restaurants I've visited.)