In Budapest, it is worth it to be unambiguously, if only to look at the historical monuments and architecture of past centuries, I personally did not see such a beauty of the cities almost anywhere. Hungarians are very careful about their history and thanks to this, a huge number of monuments, attractions and interesting places have been preserved. Thanks to the legislation of the country, the historic part of the city (and these are two thirds of the city itself) is forbidden to build up with new buildings without additional harmonization, and most importantly, new buildings cannot be higher than historical. Be sure to visit the Cathedral of St. Stephen (or Ishthan, as Hungarians themselves call him).
In it, by the way, the main shrine of the country is stored - the chopped hand of St. Stephen, which is depicted on the coat of arms of the state and it can be seen to the sophistication, the truth is to admission to the cell, where the relic is stored in time. The building of the Parliament of the Republic, which stands on the very shore of the Danube looks amazing.
By the way, a walk on the river tram in the Danube, this is a terrific way to explore the city a quick look to understand what to see first of all, and what to leave for later, perhaps generally until the next time, because the week to get acquainted with the city will few. If there is a desire to see the city from a bird's-eye view, then you should visit the fishing bastion, from where a beautiful panorama of the foot (left-bank part of the city) and Danube opens.
To compare according to the historical and cultural component, the excursion to Budapest can be compared only with a trip to Vienna on the saturation of artifacts for one square meter, but in Hungary everything is cheaper, if only because they retained their national currency Forin. And probably, you should not go there with children. Children are not as interesting historical values, so they quickly get tired and will not let you really see the capital.