Just got back from Budapest and would like to offer a couple thoughts/tips.
We stayed at one of the Superroom apartments (on Kossuth Lajos ut) for 4 nights and really appreciated the accommodation. It's perfect for the budget traveler, as we paid about 20 USD/night per person. A great deal for such an amazing location, and an adequately furnished apartment. The first two nights, the other room in the apt. was taken by some friendly travelers, but the second two nights we had the place to ourselves.
Peter and Marton are extraordinarily friendly and helpful guys--I can't stress enough the benefits of having them as a resource. We found that their recommendations were always better than Lonely Planet's (or other guidebooks). We really appreciated that Peter took the time upon our arrival to show us the best way to get to places, and the places he recommended were spot on (e.g., Menza, Paprika). Also, the apartment is near Cafe Auguszt which we wildly preferred to Gerbeaud, and it was a nice place for breakfast or a mid-afternoon pick-me-up.
Another tip: if you're going to Parliament do as others have suggested on this forum--make a reservation (email firstname.lastname@example.org , email@example.com asking for a specific time and date for the offered tours), it lets you skip the sometimes-long line for tickets in the morning.
Also, the 7-day transit pass is only about 500 forints more expensive than the 3-day tourist pass, so if you're there for 4 days, don't buy a 3-day plus a 1-day.
We really enjoyed Szechenyi Baths, but might recommend against the Aroma Relaxing massage (one of the newer ones they're offering, I think), it was nice and not too expensive as far as massages go, but not that amazing. Be sure to go around and around in the circular current in the cooler outdoor pool for some fun...everyone ended up shrieking like children.
The statue park is a long haul out there for not much to see--what is there is definitely interesting, but right now a good chunk of the exhibit is under redesign of sorts (results in a cheaper ticket, but the whole thing can still be seen in 20 minutes).
The Labyrinth is definitely a tourist trap of sorts, but we still had a lot of fun going through it with lanterns after 6pm...just take it for what it is.
If you go to the House of Terror, I would recommend an English Audio Tour...we didn't do it and still took a lot away from the museum, but if we were to do it again, we definitely would've gotten the audio tour.
Eat on Raday ut one night, lots of options (even if they're a bit touristy) with a good variety on the menus. We had a friendly waiter at Cafe Leroy who also had lots of info. about the city to share and he gave us a try of Unicum. The food wasn't the best that we had there (I really liked the updated goulash at Menza and the chicken and plums at Paprika), but it was definitely good, and nice to sit outside with blankets.
We also ate at Gundel's sister restaurant, Borvendeglo. It was good, but also didn't live up to the hype for us.
Other than that we did the usual things, and lots of walking around. It was a truly amazing trip. We found the people of Budapest to be much friendlier and more helpful to us English-speaking folks than we anticipated from other people's comments, and definitely appreciated the kindness we got from most of the people there.
Just a question--have others found Gerbaud to be a let-down?
Hope some of these tips might help...