The usual way

1. Castle Hill - interesting old houses, churches, exhibitions.

2. Pest Center - Vaci utca (street) and Vorosmarthy square (a shopping area with nice Art Nouveau houses), St. Steven's Cathedral (the second biggest church in Hungary), 1500 year-old Roman ruins right at the foot of Erzsebet hid's Pest side, and a Turkish Bath right in the city center (Rudas).

3. The Jewish Budapest
Discover the footprint of the once biggest Middle European Jewish Community around the Dohany utca (street) Synagogue.