Returned from Budapest, my recommendations:

Me and my husband just got back from a 12 days Hungary trip. I read so
much here, when we were planning, that I felt I have to write some
suggestions: We were in Pecs, Szeged, Sopron, Debrezen and Budapest.
The best city was Budapest of course, but I liked the smaller ones
also, especially Pecs was a surprise and I heard it will be Europe
Culture Capital in 2010. We stayed in small hotels, homestays on our
trip. We had 2 very good accomodation on our trip: In Szeged the
Kanfalussy Family's small Pension (kanfallusytourism.hu) we stayed at
and it was great, the food they made for us was so delicious and we
had a real Fishsoup also... In Budapest we stayed at the www.superroom.fw.hu
(also known as SuperChargedRoom) and it was also excellent. We paid
very little and we had a beautyful and big double room with a balcony
next to the DEKA FERENC TER, which is the main square of the city. It
was facing to a silent street so it wasn't noisy, even though we were
in the lively center of the capital. The owner /Marton/, who lives in
the apartment studies economics and he was absolutely helpful, we were
keep on asking our "stupid questions" , but he always took the time to
answer. He made our stay perfect, recommended us concerts,
restaurants, places to visit. If you stay there then listen to his
recommendations, it's really useful! We were at the 100 Gipsy
Orchestra's Concert and we were at an event in the Palace of arts,
it's amazing... We ate out a lot and the food was gorgeaus
everywhere... We took the lidego one day up to the John's Hill, from
where we could enjoy the best panorama of the town. We have visited
Szentedre and also we went to Eszergom.
I've collected 10 things not to miss while being in Budapest:
1.)Paprika Restaurant
2.)Lidego (chairlift)
3.)Gellert's Hill
4.)Castle Hill
5.)Andrassy boulevard
6.)Raday and Liszt Ferenc utca
7.)Heroe's square
8.)Palace of arts
9.)Margaret island
10.)Belvaros
I hope it helps for other visitors, and I'm pretty sure you'll enjoy
your time there!