Reddit mentions of Korea And Her Neighbours...

Joseon era:

• A Review of Korean History, Vol.2: Joseon Era; Woo, Han Young (2010)
  
• Sources of Korean Tradition, Vol. 1: From Early Times Through the 16th Century (Introduction to Asian Civilizations); Lee, Peter H. (ed) (1996)
  
• Sources of Korean Tradition, Vol. 2: From the Sixteenth to the Twentieth Centuries; Lee, Peter H. (ed) (1996)
  
  I prefer the 'Review' more, but it might come across as a little dry. I feel that it does a fair job of discussing a number of topics related to the creation and running of the Joseon Dynasty, breaking the dynasty up into smaller components and then focusing on some areas (arts, military, cultural practices) within those smaller time frames. 'Sources' for me came across as more academic than 'Review' but you might enjoy it more. 'Sources' includes translations of primary sources, which is helpful, while 'Review' includes images such as paintings and maps.
  
  General:
  
  
• Korea Unmasked: In Search of the Country, the Society and the People; Rhie Won-bok (2005)
  
  A comic book that goes into the 'making' of Korea and Korean culture. I have some reservations about this one but if you don't take it too seriously it can be a fun and easy way to get introduced to a number of topics related to Korea.
  
  'Modern' Korea:
  
  
• The Dawn of Modern Korea; Lankov, Andrei (2007)
  
• Korea Through Western Eyes, Book, Written in English; Neff, Robert (2009)
  
• The Two Koreas: A Contemporary History; Oberdorfer, Don (2013)
  
• Korea's Place in the Sun: A Modern History; Cummings, Bruce (2005)
  
• The Koreans: Who They Are, What They Want, Where Their Future Lies; Breen, Michael (2014)
  
• Korea And Her Neighbours...; Bird, Isabella (2011; original 1897)
  
  Lankov's book is a collection of newspaper articles he wrote entertaining subjects like the story of Korea's first automobiles, the introduction of the first telephones, etc. Easy to digest and they offer a glimpse of what society was like at each point in time; not a 'serious' book on Korean history, though. Neff's book was a chore to get through and it felt like no editing had gone into the book before publishing. If I'm not mistaken this also started out as a series of articles for one of the local newspapers; the transition from article to book did not go quite as well.
  
  It's probably been 10 years since I read the books from Breen, Oberdorfer and Cummings, which makes it a little difficult to write a lot about them. Cummings I know gets criticized for being pro-North Korea in his writing, so that's something to keep in mind, while Oberdorfer I think was a correspondent living in Korea so may have a more 'eyewitness' approach to some of the events. Bird's book is a description of her travels in Korea during the Joseon period and I remember it being an interesting read. Not a balanced historical account by any means - and it obviously suffers from being written from an outside perspective at a time when ethnocentrism was more prevalent - but it may be an alternative to consider. You should be able to find a .pdf copy of that one online.
  
  
• Fifteen Years Among The Top-Knots: Or Life In Korea; Underwood, Lillias H. (2007, original 1904)
  
  Haven't read this one, but I've seen others mention it in the past. It's another first-person account from Korea at the cusp of the 20th century, this time from the perspective of a medical missionary. Again, not an objective history book, but if you prefer first-person narratives it may at least be worth a look. A .pdf copy has been published online, this one by the University of Oregon.
  
  Edit: One I forgot to mention, but which I've also heard is used in some English-language classes on Korean history/studies:
  
  
• Korea Old and New: A History; Eckert, Carter J. (1991) (I just noticed this is also mentioned by seaturtles7777)