The original monastery is thought to have been where Christ Church now stands, and in the 1980's archaeologists found evidence of a graveyard there dating back to the late 7th century.
Tradition has it that this is where St. Frideswide was buried, and in 1180 the prior of the (by then Augustinian) monastery had her bones disinterred, and laid with great ceremony in a reliquary which was displayed in a shrine to which pilgrims flocked, hoping for miracles. They were not disappointed.
A later shrine (1289) was broken up during the Reformation in the 1530's, but many pieces from it have been found over the past hundred years or so, and it has been reconstructed in Christ Church Cathedral. It stands in the Latin Chapel, in front of a wonderfully detailed stained glass window telling the story of her life, designed by Edward Burne-Jones, the Pre-Raphaelite artist, in the 1850's.
As for her bones, they were dug up in the reign of Mary Tudor, and kept in two silk bags.
A few years later, when the Protestants were again in the ascendant, and the veneration of saints severely discouraged, St. Frideswide's relics were deliberately mixed up with the bones of another woman who had been buried only recently in the Cathedral, and they were re-interred together in "the upper part of the church towards the east".
This is where the shrine is now, but a little to the south of it, in the Lady Chapel, there is also a dark paving stone in the floor carved simply with the name Frideswide, and it is here that the anniversary of her death is commemorated on October 19th each year.
Here is some history of Christ Church, from the Cathedral website. According to Once I Was a Clever Boy, St. Frideswide will be honored this week on her feast day.