If you are searching for a good place in Budapest to have a breakfast I can recommend to you Café Déryné in the heart of Buda. It is located right at Krisztina Tér, which is behind the tunnel and on the foot of the Buda Castle disctrict.
The offer of Café Déryné is large and you can find a breakfast for everybody, continental or English they have everything. Also very good is the coffee variation and the interior design is close to perfect. All this sounds like an expensive first class place to you? It is not, the prices are average but the service and the quality of food are great.
Krisztina tér 3
District 1, 1013 Budapest.
Reservations: +36-1 225 1407
Opening hours: Weekdays 07:30 till 23:00, weekends 07:30 till 0:00
Or visit their website