The town is mentioned by the Duke of Buckingham when he decides to flee to Brecknock. Originally promised an Earldom (of Hereford ) by Richard if he supported Richard's bid to become king, Buckingham comes to the realisation this will never happen. He also begins to reconsider his support of the king, and on being ordered to murder the two young princes by Richard he doesn't immediately jump to follow orders, instead rather vaguely asking if he can get back to the king on that idea;
"Give me some little breath, some pause, dear lord, Before I positively speak in this. I will resolve you herein presently." Richard III, Act IV Scene ii.
Remembering what happened to Hastings, another former supporter of Richard, (spoiler alert - he died, beheaded at the order of Richard III), Buckingham decides to flee to Wales. There he plans to hide out and then join forces with Richard's opponents. After a failed rebellion he is captured and, as he feared, beheaded on the order of his former friend, King Richard III.
Brecon has another link to Shakespeare as well. It is the location of Trebarried House in the Brecon Beacons, a stately home Shakespeare is believed to have stayed in while he was writing A Midsummer Night's Dream. It has been reported that a visit by Shakespeare to the nearby caves at Cwm Clydach (Clydach Gorge) was the inspiration for the setting of the play.
Page:
"Wives may be merry, and yet honest too." Mistress Page speaking in the Merry Wives of Windsor, Act IV, Scene II
Page is the family name is a group of characters in Shakespeare's Merry Wives of Windsor, including one of the titular Merry Wives - Mistress Page.
The Merry Wives are Mistress Page and Mistress Ford, two smart women who, upon learning a man named Falstaff plans to seduce them as a way to solve his financial woes, conspire to turn the tables on him and show him to be the fool he is.
Falstaff writes a letter to each of the women, in the hope of seducing one or both of them. The wives meet up and compare letters. Discovering they are identical they decide to have some fun, and teach Falstaff a lesson. They invite him to come to Mistress Ford's house while her husband will be out. When he arrives, the clever women convince him the men are returning home early and so persuade him to hide in a laundry basket. While he is in the basket, it is carried out to the muddy river by the housemaid and the contents, including Falstaff, are tipped into it.
Despite this, Falstaff is persuaded by the wives to return and this time, when Mistress Ford's husband returns earlier than they had told Falstaff he would, they persuade Falstaff to disguise himself in the clothes of a servant's elderly aunt. To their glee, it turns out Ford dislikes this elderly women and on seeing "her" begins to beat her up.
The women tell their husbands, Page and Ford, of Falstaff's plan to seduce them for their money and the two plot a final revenge on the hapless Falstaff. They persade Falstaff to meet them in a local wood where, with the help of friends and some children, dressed as fairies, they shame Falstaff publicly, with the "fairies" pinching him before all present reveal their true identities to Falstaff and tell him they know of his plan. Falstaff takes the joke better than one might expect saying he deserved the treatment he received.
As the group leave the forest, Mistress Page extends an invitation to Falstaff to join them, showing his plan is forgiven, if not forgotten.
"Let us every one go home, and laugh this sport o'er by a country fire; Sir John and all." Mistress Page, Merry Wives of Windsor, Act V, Scene V