Why didn't Anne Hathaway go with William Shakespeare to London?

This is a fair question, but we really don't have enough information to be able to do more than guess. It may have been prohibitively expensive to buy a house big enough for the whole family in London, especially early in Shakespeare's career. Anne may not have wanted to sever her connections with friends and family in Stratford. The Shakespeares may have felt that Stratford was a better place to bring up children. Anne may have been nervous about learning how to live in the big city as opposed to a country town. These are only guesses.