From the cloister we can access exhibition halls and other spaces reserved for cultural programs and events. In addition to the Academia Hall, the Estudi General and the Oberta Hall, which house a large number of temporary exhibits in the La Nau Cultural Center, the ground floor also holds the main lecture hall, with its impressive coffered wood ceiling, and the Matilde Salvador theater.

On the first floor we find the Martínez Guerricabeitia Hall, which houses exhibits with works from the magnificent contemporary art collection donated to the Universitat de València by Jesús Martínez Guerricabeitia and his wife, Carmen García Merchante, in 1999. This space has had various uses throughout history. For a little over a century, until 1850, it housed the classrooms of the Academy of Fine Arts. Later, between 1872 and 1877, came the museum of Natural History, together with an astronomical observatory, inaugurated in 1909. Everything disappeared in a dramatic fire in May 1932.

On the third level of the building is the Las Vigas Hall, which is accessed from the rectorate staircase located near the entrance on Calle La Nau. Recently remodeled for use as an exhibition space with interesting and attractive architecture, it is named for the lattice of beams (or vigas) on the ceiling.