My favorite architectural building in Budapest was definitely Parliament with it's blood red dome & sharp spires sprouting towards the sky. We didn't tour the inside due to the fact that I read it is difficult to do an English tour and non-Europeans get charged almost double the price. This rubbed me the wrong way so we explored the outside & took delight in a odd optical illusion attraction behind it & the Shoes on the Danube beside it instead. If architecture is part of the reason you look forward to travel you MUST see this building.
Some of the best views of Parliament are from The Fisherman's Bastion and from across the river. To get the Instagrammable photo across-river take the metro line to the stop called Batthyany Ter on the red line #2. When you walk out Parliament will be immediately across the river from you. Don't forget to take photos at the Kossuth Lajos Ter stop as well which will drop you off right at Parliament.
I was surprised to read that the Neo Gothical Building is only a few years past 100 years old. Much of the building reminded me of Notre Dame with it's spire details and gargoyles. If you would like to read about some of the history of Parliament I suggest reading about the gorgeous building HERE.