The capital city of Hungary is a famous location for tourists and students and as a local in Budapest, I can definitely recommend visiting it. It is a huge city with the Danube cutting through it and dividing it into two very different pieces. Buda is the mountainous and less populated part, with amazing architecture, nature and views overlooking the river and the other side, Pest. Those who are interested in hiking and in need of a bit of silence can choose from many trails that are in the proximity of Buda. 

Pest on the other side has what I would call the real city center. It covers a relatively big portion of the city and it is full of massive, historical buildings. I usually have the experience with my foreign friends visiting Budapest for the first time that they keep asking me what each building is used for, since even residential houses and offices look as pretty as for example museums. The churches and universities are definitely worth taking a look at, but the Parliament is by far our most fascinating piece of architecture. You can enjoy the nightlife every day of the week here, because in certain party hubs, the discos and bars stay open until the morning even on a regular Monday.  For me what makes Budapest the perfect place for young people is that there is always something to do. There is either a new exhibition arriving to one of our huge museums, a special theme party organized, a concert being held, a sporting event taking place on the side of the Danube, new theatre piece being shown or some small celebration and performances held in one of the districts. The public transport in the city center is amazing, you can reach everything very fast and punctually. Another thing that is a huge plus is that most tourists from the EU or North America will find Hungary pretty cheap. Public safety is very good compared to other big capitals in Europe, so you can definitely walk around carefree most of the time.

The rest of Hungary, apart from maybe lake Balaton, that is the biggest in Central Europe is not at all well-known to foreigners. There are some other cities however where you can find lovely architecture and cultural events. The countryside can also offer the best thermal baths and wellness facilities in cities like Hévíz, Egerszalók and Hajdúszoboszló. Moreover, while Hungary certainly does not have the biggest mountains, trekking is a popular activity and you can find well-maintained trails all over the country. I would recommend exploring the nature at least close to Budapest for a few days if you are interested in nice views.