I've found that there is a lot of overlap in architecture, food, and culture throughout many European countries.  Austria, Hungary, and others are influenced by the history of the Habsburg empire,  (those super-rich people in Austria). Luckily, since the Hungarians remained stubbornly patriotic, today w are able to enjoy their uniqueness!
One thing I’ve noticed that is classic "Hungarian” is the colourful patterned roof tiles! The 11th-century Matthias church in the fisherman’s bastion is one that really shows this off. (you’ll see what I mean in the pictures). Walking up Buda hill, there is a gothic/Roman-built terrace called "fisherman’s bastion". There are so many reasons to climb all those steps, from the historical terrace to the beautiful church, and of course the breathtaking view! 
Another unique feature that Budapest has over its central European neighbours is the natural springs! In the 37° heat this girl was keen for a dip!! Yes, I melted. But with the 125 thermal springs that Budapest sits onto of, I was able to visit one of many bath houses to cool off. Szechenyi being my heat defeat of choice, I had the option of 3 massive outdoor pools, 15 indoor baths, and 10 sauna/steam rooms, all  varying in temperature, and all within the beautifully "Roman" complex. Grand, elegant, and crowded; but SO very worth it.
Last but not least, the incredible parliament house! Sounds boring, but I promise it is not! The tallest and largest building in Budapest, it looks like a giant temple mixed with a palace! And to top it off, it lights up at night into some sort of glowing golden amazement! 
I saw a few more things, but these were definitely my favourites!

2 days, combined 42,000 steps, and I’m off to Croatia! Bring on the coastline!