If I want to go visit the Parliament in the early afternoon, would you advise that I buy tickets in advance online, show up early to the ticket booth (in case of large crowds), or just show up right before I want to go in (if there are no crowds)?
They have just finished renovating the facility and the grounds and it is beautiful. When we went this site wasn't available, but if I were to go now I would start here: http://www.parlament.hu/web/latogatokozpont/jegyvasarlas . To buy in advance they link you to a ticket agent called Jegymester. I buy concert tickets on Jegymester all the time and have had not issues at all. Yes, I would buy in advance and arrive early. Nice tour
I wasn't the original questioner but glad I read this--I went ahead and booked my ticket, sounds like there can be quite a line and I don't want to waste time. Jegymester was easy to use and cost in USD was $18.10. I figure while I'm in that area I'll also see the Museum of Ethnography before heading on to Falk Miksa for an afternoon of antique shop browsing, then the House of Terror.
You want to be sure that you visit Pinter Antiques and wander the basement maze of old stuff: http://www.pinterantik.hu/en/home .
From the Parliament down Falk Miska to Szent István körút where you will find a stop for the 4/6 Tram. http://budapestcity.org/11-egyeb/utcak-terek/Jaszai-Mari-ter/kep-nagy.jpg
Take it leading away from the River. OR, you can walk up Szent István körút to the next stop of the 4/6 Tram which is in front of the Nyugati Train Station. http://www.budapest.com/w/assignables/galleries/328/western_railway_station_1.jpg
This is the train station designed by Eiffel’s company prior to the Eiffel Tower.
There is some other interesting architecture along the way like the Comedy Theater http://static.panoramio.com/photos/large/54824279.jpg and http://vigszinhaz.hu/short-history/ ; and you will get a feel for some non-tourist orientated areas.
Then board the Tram and get off at the next stop; The Oktogon. From the Oktogon you can either walk up to the House of Terror http://www.terrorhaza.hu/ or ride the M1 for one stop (I would walk).