My husband and I are going to spend four nights in Budapest in the beginning of June. We love good food and want to find some moderately priced to splurge level restaurants in Budapest. We are staying on the Pest side at the Gerlozy. (I posted a request for Vienna and got some good answers, so I thought I would try my luck with Budapest.).
In my research so far, I have come up with Cafe Kor, Gundel, Borkonyha, and Atakam. Does anyone recommend these and what others should I try? (We have been to Europe on numerous occasions, especially love Italian and French cuisine but we have also enjoyed Croatia, Spain and Turkey).
Also, does anyone know the popular dining hour time?

We had a delicious lunch at the "Muzeum Café and Restaurant". There were white table cloths and the place seem to be patronized by Hungarian businessmen. It is on the Pest side of Budapest. I believe we had the traditional Hungarian Goulash soup. I do not know the other restaurants you mention. The Muzeum has a website http://muzeumkavehaz.hu/?page=kezdolap

I would absolutely recommend The Bock Bistro. It is right next to the Corinthia Hotel on Erzsébet krt. 43-49, 1073 Hungary

You must have a reservation to get in, but it will be an unforgettable dining experience. They have daily specials, but I will some things are always on the menu such as the Cold goose liver in its own fat (starter) and the Esterhazy cake (dessert). DH had a starter that was an elevated version of Lecso, a sort of stew with peppers, onions, and sausage.

http://bockbisztropest.hu/en/

You must try a ruin bar -- our favorite is Mazel Tov -- try to be seated in the 'back yard' area and don't be afraid to be adventurous with what you order. We were there in 2015 and returned again on our first night in town this past October. http://mazeltov.hu/en

On the advice of a tour guide last year we ate at Fulemule (Nightingale). We loved the friendliness and authentic food. Easy to get there by public transit. https://www.facebook.com/fulemule/

We liked Ket Szerecsen this year near our apartment -- mainly locals at dinnertime. Our food was exceptionally good and service was friendly. Make reservations. http://ketszerecsen.hu/?lang=en

And we had lunch twice at Jedermann because we happened to be in the area. If you go with the 2-course daily special, soup and a generous-sized main course for under $4 USD, you can relax in the uber comfortable jazz space and recharge fro the afternoon. https://www.facebook.com/Jedermann-154462294573108/

Both years we made a stop at Cultivini to try small tastes of Hungarian wine – the staff is super friendly and knowledgeable; pay by the pour. No pressure to purchase bottles. http://www.cultivini.com

We ate at Café Kor in October too; I wouldn't go out of my way for it -- good food and service, but not otherwise very memorable.

And if you are looking for a tour guide, Anna is awesome: https://ourbudapesttours.wordpress.com/

Can you tell I love Budapest??

Thanks for the help. I made reservations for Kiskakukk,
Bock Bistro, Borkonyha and Ket Szerecsen. Can't wait to go!