http://www.bibleplaces.com/holysepulcher.htm

"First-Century Tomb

The best piece of evidence that the tomb of Jesus was in this area is the fact that other first-century tombs are still preserved inside the church. Called the "Tomb of Joseph of Arimathea," these burial shafts (kokhim) are clearly from the time of Christ's death and thus attest to some kind of burial ground in the area. Combined with the evidence from tradition, this church is most likely the true location of the Christ's death and burial." This is the site the church is built around.

also from that website:

"The Garden Tomb

While officially the Garden Tomb Association only maintains this as a possible site for Christ's burial, some tour guides of the site are very convinced. They note the large cistern nearby, which proves the area must have been a garden in Jesus' day. They maintain that there are marks of Christian veneration at the tomb which also prove its sanctity throughout the ages." This site was apparently discovered in the late 1800's - a tomb in the side of a rocky escarpment.