Stratford-upon-Avon is the ideal location for any Shakespeare fan. The city is the bard's birthplace and still has many historic homes open to the public. Anne Hathaway's Cottage may be the best preserved and includes open fields and forest paths. For true fans you can stop by Holy Trinity Church to see Shakespeare's grave, or visit the Shakespeare's Birthplace, though this is more of an interactive experience than historic site. It is worth it to see the garden players, who take requests.
Located on the river Avon is the Royal Shakespeare Company and Theatre, which allows you to tour their stages and see costume galleries. The towers provide panoramic views of the city and surrounding country. If in season, it is worth seeing one of their productions. If you can't make it to Stratford-upon-Avon they occasionally tour and can be seen in London and other cities.