1.Take the Funicular up to the castle district and visit the Royal Palace, home to the National Gallery. The Fisherman's Bastion and Matyas Church and Military Museum are also in the district. Grab an ice cream at the Ruszwurm cafe.
2. A tour of the Hungarian Parliament.
3. Heroes Square and the surrounding city park. Also nearby are Vidam Park (Amusement Park Hungarian style) and the Zoo and the Szechenyi Baths.
4. Vorosmarty Square (stop for a cake at the Gerbeaud Cafe) and Vaci Utca.
5. The City Market (nagycsarnok) - a real taste of Hungary.
6. Margit Island - in the middle of the Danube and oasis of calm in the heart of the city.
7. Gellert Hill for the Citadel and beautiful floodlit views of Budapest at night.
8. The West End Centre for shopaholics.
9. Take the lift to the gallery at the top of St. Stephens Basillica for panoramic views of the city.
And this is just the tip of the iceberg.
Quick Tips:
Get hold of the Budapest Card for hassle free travel and free or reduced entries to the best museums and galleries.
For a real taste of Hungarian cuisine, visit the Karpatia, Apostolok or (if you have a reasonable budget) Gundel Restaurant. Or for something simple grab a Langos (a speciality bread) at the city market.
Budapest is well known for its outdoor cafes and restaurants along the Duna Korso (Danube Embankment).
Best Way To Get Around:
Public transport is excellent and will get you to all the major sites. The city has an extensive network of buses, trams and trolleybuses, supplemented by 3 metro lines and 5 suburban railway lines. Ensure you have a properly validated ticket though, as tickets are checked frequently by roaming inspectors. They will happily dole out fines to people abusing the system or travelling without valid tickets (use the Budapest card for hassle free travel).
Budapest is also a city to stroll in. Avoid driving unless you are familiar with Hungarian drivers!