You can visit the Hungarian Parliament almost every day (see exceptions below), but the places in tours are quite limited, and the only way to visit the Parliament in Budapest as a tourist attraction is if you are in a guided tour (offered by the Parliament itself with professional guides).
Hungarian Parliament – photo: Kay Eber
The Visitor Centre of the Hungarian Parliament is the official tourist office of the building where almost half a million tourists take a visit a year.
Opening Hours of the Parliament Visitor Centre
1st April–31st October
Monday–Friday: 8.00 a.m.–6.00 p.m.
Saturday–Sunday: 8.00 a.m.–4.00 p.m.
1st November–31st March
Monday–Sunday: 8.00 a.m.–4.00 p.m.
The Parliament in Budapest is open on the following days (unless closed for an upcoming or ongoing state event for delegations / protocol events):
Opening hours in high season, between May 1 and September 30
Monday–Friday: 8 am – 6 pm
Saturday: 8 am – 4 pm
Sunday: 8 am – 2 pm
Opening hours in low season, between October 1 and April 30
Monday–Friday: 8 am – 4 pm
Saturday: 8 am – 4 pm
Sunday: 8 am – 2 pm
Basically that means that the gates of the Parliament in Budapest are open every day of the week all year round, except for special events taking place in the building of the Parliament. In other words, the Parliament is closed during parliamentary sessions, miscellaneous official receptions, and on some national holidays.
The Hungarian Parliament used to be traditionally open to the public on certain national holidays but not any more (national holidays are like March 15, August 20, October 23, New Year’s Day (January 1)). Anniversary of the 1848/49 Revolution (March 15), Easter Sunday, Monday, Labor Day (May 28), Whit Monday, St Stephen’s Day (Aug 20), Proclamation of the Republic (October 23), All Saint’s Day (November 1), Christmas (December 24, 25, 26).