I do not have one recommendation in particular, but we just loved the Turkish food, the mezzes, the fresh ingredients, and the combination of spices. We thought it was one of the world's underapprecaited cuisines.

In istanbul, I enjoyed meals at:

Pasazade
Ahirkapi Balikcisi (fish only, and only a few tables) and
Imbat

All are in Sultanahmet.

Have a look at my trip report from a few years back http://www.fodors.com/community/europe/seamus-istanbul-trip-report-may-2005.cfm
One thing I remember being especially delicious was the breads.
Enjoy your time in this amazing city!

I mention a few of restaurants in my trip report; click on my name to find it. One would have been even better with more than the two of us for the meal as it started with 18 mezes.

As far as I am concerned there are no "good" let alone "excellent" restaurants at Sultanahmet with the exception of the restaurant of the Four Seasons hotel which is over-priced.

I off-hand recommend the following :

Changa
Musee de Changa
Ulus 29
Beyti
Assk Kahvesi
Mia Mensa
Sunanin Yeri (ferry from European side)
Oz Kilis
Akdeniz Hatay Sofrasi, (call and order at least two hours before for special lamb)
Bursa Garaj
Alekonun Yeri/Deniz Park
Sardunya
Borsa (near istanbul Hilton)

Do not eat under the Galata bridge.

Hamdi at Eminonu is touristic but has exceptional view and acceptable food.

Namli at Karakoy is the only Turkish Deli and has interesting choices for breakfast and lunch.

Next to Namli, Gulluoglu is the only good baklava store in Istanbul. (Hamdi restaurant's baklava store is not too bad either)

You should get your Turkish delight at Hacibekir (Sirkeci and istiklal stores) or at Kosla (next to Gulluoglu at Karakoy, at Istiklal and others)

The best quality Turkish Royal Ottoman cuisine is at the Kempinsky Ciragan palace Hotel but is very expensive. Asitane restaurant next to Chora Museum is fine for this cuisine also and is reasonably priced.

Kanaat restaurant at Uskudar has the best Turkish home cooking with possibly fifty or more options. I love the Ozbek Pilav which is unfortunately rather greasy and has lots of calories.

Try Lykia, Doluca Kav, Doluca DLC wines at medium price range preferably, their Okuzgozu, Kalecik Karasi and Merlot grapes in red and Narince, Emir grapes in white. One of the good more expensive wines is Kavaklidere Selection but I do not remember which year was the best. I do not like the Corbus or Corvus wines which I think are over-rated. Gulor is also overpriced. Some Urla, Sevilen, Karya and Majestik wines are also good.

Thank You - We do not plan on staying in the Sultanakmet area for our meals. We are staying in this area only because of its proximity to the various sites and reasonable hotel rate. I do think we are closer to the Sirkeci area but I am not sure as the different areas are a bit confusing to me. I appreciate all the guidance.

otherchelebi is the guru of all things Istanbul or Turkey in general, jk1348. We are so lucky to have him.

We enjoyed a restaurant not that far from your hotel, Karakoy Lokantasi (http://www.karakoylokantasi.com/). It's across the Galata Bridge (not on!) near the Karakoy pier-you can avoid a taxi if you like.

You can get the street address from the website, but all you have to do to get to the area is hop the tram down over to the Galanta stop. Walk along Kemankeş Street for about two or so blocks. Actual address: Kemankes Caddessi, Karaköy The map is on their website. There are plenty of reviews on "foodie" sites.

Get a reservation so that you're not stuck upstairs. Locals have most of the reserved tables downstairs where there's easy access to mezze viewing. Telephone: 90-212-292-4455.

We actually never took the tram to the Karakoy. For our first visit,we were staying in the hotel above the restaurant. For our second visit, we were in Sirkeci near the Gulhane stop, and it was a snap to walk downhill and across the bridge to the restaurant. On our way home, we still walked the bridge back so we could check out all the fishing action one last time, and then took the tram up to our stop.

If you are a foodie, check out Istanbul Eats tours, too.

Thank you - we are actually going to go on an Istanbul Eats tour the Monday or Tuesday we arrive. I think we will try your suggestion for Sunday night since it is fairly close to the hotel and we will be a bit jet lagged.

OMG-you had me scared for a sec with the "we arrive" part of the food tour statement. I could not imagine doing the Old Town tour with jet lag--you need your full appetite. I re-read and now understand.

Karakoy Lokantasi tip: I really liked the fried lamb's liver (hot started category). No one seems to know how to cook liver correctly in the US anymore, so this was great for me. First time it was good; second time, it was even better. Husband, who detests liver, thought it was excellent.

Food tour tip: Go lightly on the baklava stop if Angelis puts it near the start of the tour. There were so many things I would have downed more of had I had a bit more room in the belly. Another thing--the sparkling water was REALLY good. We're sort of San Pellegrino fanatics, and whatever it was that Angelis bought, it put SP to shame.

Give Angelis a hug from me. Of course, he won't know who I am, and he won't need a hug anyway. Every store owner we pass comes out and hugs him. He's so thin he must be bruised by the end of the day.

I've eaten in several pleasant restaurants in Sultanahmet. There's the Sarnic Restaurant, built in an old cistern - very atmospheric (food nothing special, but OK) on Sogukcesme Sokak. Also on that street is the Garden Restaurant which is a lovely courtyard to have lunch in. The Yesil Ev restaurant is also enjoyable, as is the Karakol Restaurant just inside the main entrance of Topkapi Palace (make a reservation before you turn up in the evening, or the armed guards may not let you in). The Mosaic Terrace Restaurant atop the Eresin Crown hotel is a lovely spot for lunch on a hot day. There are a number of other cheaper restaurants. Dismissing all the dozens of restuarants in Sultanahmet and always eating elsewhere would be a mistake, IMO.

We had dinner at the fish restaurant mentioned by kja in a previous post and really enjoyed it. Food was very good and the place had a fun atmosphere. The Lonely Planet Istanbul book described it as a restaurant locals will go to Sultanahmet to dine there. A reservation is needed.

I agree with alessandraZoe. karakoy Lokantasi is good. My daughter eats there frequently. The liver is called "Albanian Liver" or "arnavout Jeeairy" as pronounced in Turkish if fried. If grilled it is called "yuprock jeeair". The city of edirne is famous for its liver dishes.

in terms of visitors believing that some Sultanahmet restaurants are quite good, I liken it to a European having its first few tastes of baby back ribs at a diner or two in America, or a Russian who has only had McDonalds hamburgers having a hamburger at Carls Jr. and believing it to be representative of good and typical american cuisine. the wxamples can extend easily to jambalaya, pastrami sandwiches, etc.

I have been to new York and London maybe thirty times each in the last thirty years but do not have the guts to say that there are some really classy restaurants around Times Square and Piccadilly Circus and that you do not need to go far for good food.

We loved the Mosiac restaurant which was mentioned above for dinner-great food and atmosphere!