Lovely city for a short break. The mighty Danube separates Buda with its castle district from the much flatter Pest with its fine buildings and museums.
All the details of what to see can be viewed on the Balkan History website.
Highlights include the Military History Museum with its collection of uniforms, paintings and equipment. It is housed in former barracks in the far corner of the castle district. The National Museum in central Pest is much stronger on the earlier periods with good collections of arms and armour. Both museums have plenty of English translations and small but useful shops that sell good value booklets.
Other sights include Gellert Hill named after the unfortunate Bishop, who got rolled down the hill that dominates the city, in a barrel of nails. The Citadel on top houses a small museum of the WW2 battle for the city. Finally don't miss the Heroes' Square with its monuments to the nation's major historical figures.
In the evening I would recommend the stunning 19th Century cafe/restaurants with their tasty traditional cusine and full bodied Hungarian wines.
Me and the inevitable Hussar outside the military museum.