To explore Budapest, how many days to see the sights?
Three days is a bare minimum. The more the better.
As many as you possibly can. It is a wonderful city. We have been for 3 days and 5 days and are hoping to go back soon for a longer stay!
We spent three days and could have used one or two more. Depends on what "the sights" are for you. When James reads your question, he'll offer you lots of scenarios based on his many visits there.
At least three full days.
2013 Trip Advisor Top 25 Destinations – Europe
2013 Traveler’s Choice Winner
2013 US News and World Reports top 20 places to visit - world
2013 Conde Nast Traveler: The 10 Best Cities in the World
2013 Lonely Planet Top 10 European Destinations
NYT Article from 2011: http://www.nytimes.com/2011/07/31/travel/36-hours-in-budapest.html
NYT Article from 2013: http://www.nytimes.com/2014/02/02/travel/wintertime-bargains-in-budapest.html
Each person has their own perception of what they like. I happen to like Budapest in a very different way than James does.
I love the thermal waters (I visit the baths once a day while there). I like the outdoor green spaces found in different parts of the city. I like walking along the Danube on the Buda side. I like stopping in for lunch at the covered market. I like finding the quirky bronze statues here and there. I find the varied history interesting. I'm thoroughly intrigued by the difficult-to-crack language and mien of the Hungarian people.
Personally, I think that visiting the Jewish quarter (including the small museum and Holocaust memorial) is a must, as is spending a few hours exploring the Castle hill and Buda below. I also think that the City Park is worth a bit more time to explore, than just seeing Heroes Square and rushing to the Szechenyi bath. I admit that, when I stepped inside, I was under-impressed by the Parliament and more fascinated by the covered market.
In addition, there are interesting and easy trips you can do, with Budapest as your base/jump off point:
Godollo, the Danube Bend, Etyek, etc.. I actually split the Danube Bend into two days: 1. Vak, Esztergom and Visegrad. 2. Obuda, the Roman site of Aquincum and Szentendre. Eger is a great 1-2 nights side trip.
So, in answer to your question, I do think that a minimum of 3 full days is needed to experience Budapest fully and decide for yourself what you liked best and what you didn't... 2 days if you are a go-go-go type of tourist.
I tend to agree with George and while Budapest is interesting, it's not on my list of cities to return to in the near future.
I was there for three nights as part of the RS Eastern Europe Tour. For me, it wasn't enough time. There were many things I didn't get to see that I would have wanted to. Others, like the Szechenyi baths and market hall, I could have visited daily but didn't have time. I did make it to Memento Park via public transportation and it was well worth it. Would have liked to spend time near Parliament, synagogues, Gellert Hill and Citadella, the Opera House. Our guide, Peter, is from Budapest and he really knew how to present his City.
If the opportunity presents itself in the future, I would go back for another 3 night stay on my own.
My first trip there about 7 years ago was a wonderful experience and I loved Budapest...however, I did not have many expectations and I did not know anyone else who had visited there,nor was I on this website... I found it to be beautiful, amazing, loved the food, friendly people and it was so inexpensive compared to further west. However, I can see how all the hype could lead to disappointment for some.