Plaza Bolívar & El Capitolio -- Pigeons, pedestrians, park benches, and a towering bronze statue of El Libertador on his sturdy steed are the hallmarks of this square city block, which was once the heart of colonial Caracas. Within a 4- or 5-block radius, you will find several important museums and cathedrals, as well as the birthplace of Simón Bolívar, the national Congress (El Capitolio), and the Panteón Nacional, the country's most important mausoleum. This area is relatively safe to explore during the day, but I would definitely avoid it after dark.
Safety Advice -- Although outwardly inviting, I recommend that you avoid El Calvario Park, which lies on the western end of the Capitolio area. In recent years, it's become a dangerous and unprotected area.