On a recent trip to Budapest (Sept 11) we went to a wonderful restaurant on the Pest side. It was called DIO restaurant and Bar
www.diorestaurant.com
we had a wonderful meal and great Hungarian wine. It was not cheap, but not outrageously expensive either. It was however good value for money. We recommended others to go here, and they enjoyed it also. The food was innovative but had a hungarian flair. Just what we had hoped to experience.

We also went to the Pierrot Restaurant (for lunch - they were booked for a private party for dinner, the night we were there) http://www.pierrot.hu/
another place to try.