There is a great deal of hustle, bustle, and moving from one place to another in Richard II--although this looks like nothing compared to the even more complicated geopolitical business that fills the Henry plays that follow it. A map of medieval Britain, such as the one found in the Riverside Shakespeare edition of Shakespeare's plays, can be very helpful in keeping track of the places and movements in Richard II, although it is by no means necessary in order to understand the play. For those who are interested, the important place names and basic trajectories of motion which occur across the course of the play are listed below.
The King's Court is in the capital city of London, which is located in the southeast part of England. Westminster Hall is in London (this is where Bolingbroke puts Bagot and Aumerle on trial in Act IV, scene i). Near the city of London is Windsor Castle, where King Richard and his allies spend time at the beginning of the play, and where Bolingbroke resides in Act V, after he becomes king. Plashy, the home of the Duchess of Gloucester, is also near London; so is Langley, the residence of the Duke of York (where Queen Isabel resides after Bolingbroke invades England in Act II, scene ii, and before she goes to London to meet Richard in Act V, scene i).
When Bushy and Greene flee from Windsor Castle in Act II, scene ii, they go to Bristol (or "Bristow") Castle, which is far to the west of London, in Wiltshire. Not far from this is Berkeley Castle, situated in "Cotshall" (or the Cotswalds), somewhat northwest of Bristol. This is why Bolingbroke can so easily find and capture Bushy and Greene after he reaches Berkeley Castle in Act II, scene iii.
Bolingbroke's invading force, as we hear from Northumberland in Act II, scene i, sails from Brittany, which lies across the English Channel to the south of England, and then sails around the south and up the east coast of England to land at Ravenspurgh, which is on England's northeast coast (we hear news of his safe arrival there in Act II, scene ii). Bolingbroke and his men then ride southwest across the northern part of England; they move nearly all the way across the country to arrive at Berkeley Castle, in the wild high western country near the border of England and Wales, where the Duke of York has gathered his small forces. This is where they meet up with young Harry Percy, and then with York, in Act II, scene iii. From here it is not far southeast to Bristol Castle, where Bushy and Greene are apprehended and executed in Act III, scene i.
When King Richard sails away to Ireland between the end of Act II, scene i and the beginning of Act II, scene ii, he presumably departs from the west coast of Wales (this only makes sense, since Wales borders England on the west, and the island of Ireland is west of both Wales and England). We do not see him again until Act III, scene ii, when he returns to the Welsh coast, landing near a northern point called Harlech (this appears in Shakespeare, due to a rather complicated transcription error, as "Barkloughly"; this should not be confused with Berkeley Castle in England, which is where York and Bolingbroke have met). When Richard learns from Salisbury and Scroope that Bolingbroke has invaded and gained power in England during his absence, he heads northeast to Flint Castle, on the northern coast of Wales, to await Bolingbroke and his men. Here, Bolingbroke finds him in Act III, scene iii, and brings Richard back with him to London.
Pomfret Castle, where Bolingbroke decides to send Richard after his deposition instead of imprisoning him in the Tower, is a long way from London: it is in the proverbially wild and desolate northern country of Yorkshire, not far from Ravenspurgh, which was Bolingbroke's landing point. This would be the right place to send someone whom you did not want to hear from again, or whom you expected might "accidentally" wind up with an assassin's knife in his throat. (That is not to say that people did not get assassinated in the Tower all the time, but it would have been easier to hush it up if you sent somebody into the wild lands of the north, instead of into the centrally located Tower of London.)