I've really been enjoying reading through "Undaunted Courage" by Stephen E. Ambrose. I've also been in love with Patrick O'Brian's "Aubrey Maturin Adventures"
I want to learn more about Captain Cook's voyages, but there are so many books out there and I dont want to get one that someone just self published and wound up on the History channel talking about aliens building the pyramids.
Why don't you get his Journals? I've read through about half of the first one. It's a fascinating look, especially the New Zealand parts.
If you're interested in a popular history of Cook, Tony Horwitz's Blue Latitudes is worth a glance:
http://books.google.com/books/about/Blue_Latitudes.html?id=PW4JbbgvxHYC
Horwitz (who also wrote Confederates in the Attic, about Civil War re-enactors) spends time visiting the places Cook had been in the present day. It's a pretty easy read, if not historically rigorous.
If you want a straight-up biography, Richard Hough's Captain James Cook is fairly well-regarded. It's pretty dry, though, by comparison to Horowitz's book:
http://books.google.com/books/about/Captain_James_Cook.html?id=4k8BEKVxDK8C
And, as /u/joustswindmills suggested, Cook's original journals are also interesting reading.
As a separate suggestion, since you're an O'Brian fan, can I recommend to you his biography of Joseph Banks? http://books.google.com/books/about/Joseph_Banks.html?id=0cIFstZ8dz4C