Plaza Mayor is, apparently, a new place in Caracas. The receptionist at Hotel Alba directed us there when they didn't have any rooms available and it was a good tip. It was not expensive (considering Caracas prices), clean, comfortable and decently equipped. Almost in front of the hotel there is a tube station Bellas Artes (trains directly to Capitolio/Plaza Bolivar) and a nice place serving delicious arepas, batidos and merengadas.
You must be careful, though, as a local guide warned us against walking in the area after dusk. General tip - the vicinity is safe, but after sunset take a cab!