You are right that Hungary could and should punch above its weight, however there are a few things it is already notable for that's worth "spreading around". 

Language: Hungarian is a unique and ancient language completely unrelated to almost every other European language. It doesn't belong to the Indo-European language family. It's a member of Uralic, distantly related to Finnish and Estonian and a bunch of very small languages in Eastern Europe and Western Siberia. 

Lake Balaton is the largest lake in Central Europe and lake Hévíz not far from Balaton is the largest swimmable thermal lake in the world. Hungary is full of geothermal springs and every town worth a damn has a bath house making use of it. Budapest is home to hundreds of thermal springs and dozens of bath houses. There are enormous cave systems underneath Budapest, many of them filled with water. Exploration of these caves is still going on. 

In terms of sports, Hungary is known for its horsemanship, horse archery and we are in the top tier in handball and waterpolo. Generally in water related sports Hungary does really well in the Olympics and overall, especially compared to its size, Hungary does exceptionally well at the olympics. 

Our food is spicy and hearty. You might have heard about goulash, chimney cakes, lángos, chicken paprikás. Hungarian sausages are excellent and some of the best in the entire world if we are being honest. The number one spice is smoked paprika powder, which comes in both sweet and hot variety. Hungary is also home to the world's first officially recognised wine region, Tokaj, which is famous for its sweet dessert wines, the wine of choice of European royalty. Louis XVI of France said "it's the king of wines and the wine of kings". Another famous wine region is Villány, known for its red wines. Hungary is a small producer so it cannot compete on the international market in terms of quantity but Hungarian wines win international awards and prizes every year. 

Hungarian inventions include the dynamo, vitamin C, the ballpoint pen, holograms, the BASIC programming language, Rubik's cube, and Hungarian scientists were instrumental in developing nuclear fission and even the fusion bomb. Look up "the Martians" a group of Hungarian mathematicians and physicists from the last century. Hungary also has a good number of Nobel prize laurates, we gained 3 more recently. 

Hungary also came up with one of history's most successful military unit, the hussar. And if you have seen pictures of 19th century military men or royals wearing elaborate uniforms with those swirly patterns, that's actually a traditional Hungarian motif that was originally used by Hungarian hussars that then became used in Western militaries across the globe as well.