There are may great books that cover this area of American and Cold War history.
These are two of my favourites:
The Right Stuff by Tom Wolfe, this is the story of the pilots who flew the early test flights that led to the breaking of the sound barrier by Chuck Yaeger up to the final flight of the mercury programme. This is a brilliantly written and enjoyable history of the early ears of the space race, a time where great pilots had to show their skill, bravery and the possession of the Right Stuff during these amazing early test flights. Definitely worth reading.
Next up is a book that cover the history of the Apollo programme. A Man on the Moon by Andrew Chaikin. This book chronicles the seventeen Apollo flights, it brings their stories to life through the voices of the astronauts, their wives and the staff in mission control who fought against the odds to keep them alive. Its an amazing read, and what is so extraordinary was that this amazing feat occurred forty years ago, and since the final flight of Apollo 17 we haven't been back to the moon again, and it is unlikely that we will get there again in the near future.
My next book is something completely different. On the recommendation of several friends I have decided to attempt some epic fantasy again. So the time has come to dip my foot into the epic Game of Thrones Saga. So today I'm going to start A Fame of Thrones by George R R Martin. Hopefully this will live up to the recommendations I've been given.