I also advice you to find a tourist guide to take you around Caracas. It will be better and safer for you.
Beautiful places in Caracas:
El Avila
Plaza Francia - Altamira, Caracas
[IMG]http://farm8.staticflickr.com/7050/6914293061_5802785aae_z.jpg[IMG]
Plaza Venezuela - Plaza Venezuela, Caracas
El Cubo Negro - Chuao, Caracas
UCV - Las Tres Gracias, Caracas (Central University of Venezuela - such a beautiful campus)
Sabana Grande Boulevard
Churches (Iglesias in Spanish language) and religious tourist spots:
Iglesia Chiquinquirá - La Florida, Caracas
Iglesia de Nuestra Señora de Lourdes - San Martín, Caracas
Iglesia Santa Capilla - Caracas
Museums:
Caracas has the best museums of Venezuela. Basically, it is one of the most important cities in South America. So many important leaders have been born in Caracas, such as Simón Bolívar.
Museo Casa Natal de Simón Bolívar - Bolívar's birth place
Museo de los Niños - Children's Museums
Museo de Bellas Artes - Museum of Fine Arts
Museo de Arte Contemporáneo (Picasso, Leger, etc)

Mseo
Other Interesting places:
Parque Ezequiel Zamora.
This place is just beautiful and has a very rich history. It was constructed under Antonio Guzmán Blanco's rule. It has beautiful European architecture, especially French. Do not forget to visit the new museum located in that place. It is truly outstanding and not so over crowded.
Take a look of this masterpiece. It's called "El Gazebo" and was brouth from Belgium to Venezuela, more than one hundred of years ago.
It is not a tourist spot and it is located in an unsafe area, unfortunately. Please, find a tourist guide. If you have trouble to find one or you need help, feel free to contact me. It is REALLY IMPORTANT for you to get a tourist guide.
Some beautiful places near Caracas (45 minutes-60 minutes from Caracas city):
Colonia Tovar town - German town founded two centuries ago