Which are the multisensory brain areas?
Association areas are exactly what you are looking for, actually.

For example, the ventral intraparietal (VIP) cortex, located in the inferior parietal lobe (along the right border of the yellow area in the image below), just on the border of the occipital lobe, integrates somatosensory (tactile) and visual information.



Image via Wikipedia

For an extensive look at the single electrode studies which illustrated this convergence, see the following article:

Duhamel, J. R., Colby, C. L., &amp; Goldberg, M. E. (1998). Ventral intraparietal area of the macaque: congruent visual and somatic response properties. Journal of Neurophysiology, 79(1), 126-136. FREE PDF