As a Hungarian citizen, I would offer you Budapest of course :).
This is a beautiful city and has many interesting venues that have to be seen by foreign travellers.
For example I could offer you the Vajdahunyad Castle, the Heroes' Square, the beautiful bridges, the Castle district on the Buda side or the Margaret Island to see. These are very nice, even with a Hungarian eye :).
I hope you will find my newest hub useful about Budapest: