I owe a debt of gratitude to a fellow board member for referring me to a wonderful guide in Budapest. I visited last fall with my husband who was there on business. I had to do my sightseeing alone as he was working. Andrew - is a warm and welcoming gentleman who loves his city and shares not only its sights, but its history in wonderful detail. You may visit his site for further details at www.guideinbudapest.com I suggest booking a day with Andrew as soon as possible upon your arrival. He will have you familiarized with this beautiful city so that you can get the most from your visit during your remaining time there.
I come in contact with a pretty good number of tourists in Budapest each year and have recommended Andrew consistently and have never heard anything but comments like yours. He very much personifies what is really wonderful in Budapest. I will make sure he reads this.
James beat me to it. I was going to give you their website too.
Another source of tours is Free Walking Tours of Budapest. They just work off tips, and have a number of different tours of the city. Tour leaves from the Vörösmarty square (tér) at 10:30 and 2:30 daily. Meeting point is at the lion fountain. (last stop of M1 yellow line)